If there’s a grace period, perhaps, however:

1. Steam does not provide installers for games, this means that whatever game you want, needs to be 100% functional and already be parsed/deployed/installed by steam on your hard drive.
2. That game needs to be DRM free, meaning that it has an executable available that can be launched without steam running or requiring any sort of authentication or input from the steam servers/services before being able to launch, play or even interact with the menus

So only the DRM free games will remain, and only the installed ones at that. Anything that wasn’t will be lost to the wind the moment the distribution service or storage (yours or theirs) bits the dust…