In first-world countries/states with earthquakes, the answer to this is often yes and yes.
A good article from 2000 in Christchurch discusses the issues: https://www.canterbury.ac.nz/media/documents/event/Hopkins-L...
The article is relevant because Christchurch had a major earthquake in 2011. I know of quite a few older buildings that were retrofitted that did not even need to be demolished (most buildings are designed to just survive a major earthquake, but often they need to be demolished due to damage, similar to writing off cars after accidents).
Christchurch did have regulatory failures because many older buildings were known to be unsafe (e.g. only meeting 10% of current code/regulations), but owners could defer fixing them up to code almost indefinitely. But that regulatory failure is being addressed in other parts of the country e.g. Wellington.
The South Island of New Zealand is overdue for a magnitude 8.2 Earthquake which will devastate many towns on the West Coast, and will affect the whole country indirectly. https://www.stuff.co.nz/the-press/news/90364889/magnitude82-...
You can sometimes see where concrete of a building has been tested for example a circular hole about 10cm across is left where a sample was taken.
If interested, next time you meet a civil engineer or someone working in the relevant department that deals with the building codes will often know relevant details about your location.
In a few minutes searching I didn't find any reference to required testing of old buildings for structural or materials integrity.
One exception is the mandatory retrofit programs implemented by some cities like San Francisco and Los Angeles.