Deconstruction is an alternative to demolition. It means carefully dismantling the constructed components of a house (or other building) so the materials can be salvaged and reused. Materials are typically removed in the opposite order in which they were installed, to maximize reuse.
A solarpunk society may have many reasons to disassemble a building. Generally reuse of existing structures (perhaps with retrofits for insulation, solar, etc) is much better than destruction but that's not always the case:
There’s tons of embodied carbon stored in those structures. In their carefully-refined materials, their transportation, and in the act of construction. Some of those materials might be very difficult to produce for a society that carefully watches its externalities and seeks to do as little harm as possible. Even renewable materials can generally be retrieved in a much more ready-to-use state. For example, dimensional lumber pulled from a stick-frame house might have some extra nails stuck in it, but it's already cut to size and will be easier to work down than a green tree, which must be cut down, transported, milled to rough dimensions, dried, possibly treated with preservatives, milled to final dimensions, and transported again. Depending on the age of the deconstructed building the older wood may even be higher quality. Furthermore, compared to mines or forests, deconstruction sites/sources of salvaged material are almost guaranteed to be much closer to the places where they'll be reused, as the best source for buildings is already-developed areas.
By carefully disassembling these structures and providing the recovered materials to their communities, solarpunk societies can build for a much lower overall cost (both environmentally and in economically), reduce the amount of construction waste it needs to store forever, and remove the threats (such as fire, chemical leaks, or structural collapse) posed by abandoned or otherwise unsafe buildings. And by filling in the buildings' cellarholes and replanting, they can rewild once-developed land, build better habitats, and restore large, contiguous ecosystems.
How this looks will likely depend on where your setting is in the solarpunk transition. If it's a post-postapocalypse with scarce resources where people are focused on surviving the year and rebuilding better, it'll look a lot more ad-hoc and rushed than a post-scarcity utopia with resources to spare.
Ideally a solarpunk society is likely to place much more emphasis on including all stakeholders in a decision up front, rather than ramming a project through the way we often see in modern day civic planning. This adds a significant delay at the outset (AKA the cheap part of the process) but once a consensus is found, execution is usually unopposed and much faster.
The process of identifying buildings suitable for deconstruction, working with any owners/stewards still around, etc will be very circumstantial for your story.
There's a little more consistency in how the actual work of deconstruction will look. Most deconstruction sites will look much like a modern construction site in reverse. Different crews work on the building in stages:
Ideally, a deconstructed structure should provide every building material used in its construction, but realistically there are going to be limitations. Shingles (asphalt roofing shingles or wooden siding shingles) are going to be basically impossible to remove intact. Some forms of insulation (especially old stuff like newspaper, sawdust, or asbestos) won't be worth reusing and may even necessitate hazardous materials disposal. Horsehair plaster can be extremely fragile and probably wouldn't be worth reusing even if it survived removal, transportation and storage. Even modern sheetrock will be a pain to salvage. Some wood will be rotten or infested with ants, termites, or other insects. Wiring and plumbing will take a lot of inspection and some careful documentation of original use before it's considered safe to reuse, and many folks will be (not unreasonably,) reluctant to use reuse it even then. Even brick and concrete can be damaged by the elements.
That said, a tremendous amount of construction supplies, from fixtures, doors and windows, to lumber and plywood can be obtained, saving both the materials and avoiding transportation and wasted space in a landfill. To get an idea of the sheer scope of materials, hardware, and stuff which might be salvaged, here's a few real life businesses which wholesale recovered construction supplies:
If a building is in good shape, and is a design suitable for relocation, its possible to save even more labor and energy and simply move the entire structure. This would be useful in any circumstance where the structure itself isn't the problem - perhaps it's just sitting on a floodplain, in a predicted wildfire zone, or in the way of a new train route or on a spot where denser housing could be constructed. This practice isn't unique to Australia, but it seems to be more established there than anywhere else I've seen. They have entire lots for what they call Relocatable or Removal homes, essentially functioning as a thrift store for old houses. Rows of Queenslanders, Colonials, and postwar houses, each up on jacks, sit in jumbled rows waiting to be bought and relocated to a new site.
This process looks something like this:
For a much more thorough guide this government resource seems to cover most steps in the process. There are also groups online where people talk about their experiences with removal homes and house shifting.
In the modern day house shifting is usually done using large trucks, and the size of each section of house moved is constrained by width the road. This adds quite a bit of work around cutting up the building, preparing the pieces to survive the journey, and reassembling them at their destination.
Shifting Houses by Barge
In some circumstances however, such as along a coastline, the shifting can be done by boat or ship, allowing far larger structures to be transported intact. For example, it is not uncommon to see houses transported between different oceanfront locations on Vancouver Island in Canada, or to nearby islands or to Washington state. Some of these structures can be remarkably large.
This business, which moves houses by barge (amongst other things) appears to operate similarly to the Australian companies, listing houses which are usually still in their original location, but also storing some at another site while they're for sale if their original location had to be cleared earlier.
Shifting Houses by Airship
It's also worth noting that transporting this type of bulky cargo overland is the exact type of work modern 'flying crane' airships propose to take on. It would take quite a bit of preparation (including inspections, structural improvements, jacking it up off the foundation and attaching it to a special platform or frame), but it's possible that these airships could transport suitable buildings the same way they propose to transport wind turbine blades, by lifting them by the winch and caring them along outside the ship just under the keel. This might even simplify the shifting process - the frame would still have to be supported from underneath, but buildings transported by air might need far less disassembly, and structures which weren't suitable for piecemeal transportation on a truck might do fine when lifted as one big, intact piece. This could mean that a solarpunk society could relocate more buildings than we can today.
A solarpunk setting might actually find itself with a large supply of removal homes. As in real life, where houses moved with government funding assistance can only be relocated to land outside of Flood Priority 1, 2 or 3 zones, a solarpunk society might identify large swaths of land which are unsuitable for long-term human settlement because of flood or fire risk.
Removal House Lots could become common, part of a system of library economics designed to waste as little as possible.
One of the main criteria for suitability for relocation is a wood frame, complete with floor, as wood handles movement and flexing better than brick and concrete, and houses built directly on concrete slabs will obviously have problems being moved elsewhere. Fortunately, stick-frame construction (on pylons or over basements) is very common in North America, so many buildings could be suitable.