This thread is for old, preferably good signs that survived reconstruction of its road, or nearby reconstruction.
I'll start with this, first pointed out by PennDOTFan in The Best of Road Signs. It survived the Iway project in Providence, RI.
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Ffarm9.staticflickr.com%2F8204%2F8267698973_4c2f1b00d3_z.jpg&hash=7f749bd7f8b928522c53612ed2e6fdb2ffa26162)
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fwww.alpsroads.net%2Froads%2Fnj%2Fnj_23%2Fpassaic.jpg&hash=26049b5ad227695213fd8154694138326df8a7d3) <- Bridge replaced in the 90s near a major mall, sign not
Not pictured, but there are random button copy signs left on roads like NY 17 (Quickway).
this US-2 shield survived a 2006 road construction project.
(//www.aaroads.com/shields/img/VT/VT19550022i1.jpg)
There were a few old button copy signs on the Long Island Expressway (I-495) in New York that survived the construction of the HOV lanes. There is one westbound at exit 39 and one eastbound at exit 58. Both can be seen on my I-495 page at http://www.greaternyroads.info/roads/nyinter/i495.
This oldie is somehow still standing through the reconstruction of the entire intersection, a railway overpass and the construction of a major hospital nearby.
https://maps.google.ca/?ll=45.473235,-73.60528&spn=84.209798,214.277344&t=w&z=3&layer=c&panoid=jGzTm1MW53CBZrT0_B58IA&cbll=45.473235,-73.60528&cbp=13,-133.64598144023682,,0,8.021409131831462
This sign, dating from the 1980s as part of a now defunct route numbering system from the 70s survived the widening of the Southern Fwy in 1999. Unfortunately, it was removed sometime in 2010. (Wollongong, NSW)
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fozroads.com.au%2FNSW%2FRouteNumbering%2FFreeway%2520Routes%2F01.JPG&hash=86f8e2d454bb6929b5c8b2f27d8d56052a2900e1)
Ozroads: NSW Freeway Routes (http://ozroads.com.au/NSW/RouteNumbering/Freeway%20Routes/freewayroutes.htm)
Here's an interesting one from the San Francisco Bay Area, Milpitas to be exact. This sign...
(https://www.aaroads.com/california/images880/i-880_nb_exit_010_06.jpg)
... was originally the exit direction sign for the Dixon Landing Road exit from northbound I-880.
When the interchange was rebuilt as part of the I-880/CA-237 interchange rebuild project, this new reflective exit direction sign was installed...
(https://www.aaroads.com/california/images880/i-880_nb_exit_010_04.jpg)
... and the old exit direction sign including the truss was moved 500 feet to provide guidance on the C/D road (visible in the background).
Granted the old exit direction sign wasn't terribly old by California standards but it is a button-copy BGS.
All photos are from the AARoads Gallery.