In the extremely unlikely chance the new clients have all of their tax returns, all of the information for the newly "placed in service" assets is on the 4562s.  So the first step is to try to get as many previous tax returns as possible.   Hopefully the client at least has the last few years; if not, ordering Transcripts of recent tax years should have that information.

The more 4562s you have, the easier it will be.  If you have most of the 4562s, then as was mentioned you can sometimes figure out the missing amounts by what is left of the depreciation.

Another thing to try is ask the family of the previous preparer to look through any paper-files.  Many tax preparers (including me) keep paper copies, and the depreciation schedules and/or previous tax returns (with the 4562s) may be available in the filing cabinet.