Oracle, MSSQL and some rarer ones (Actian Zen?) are "VSS-Aware" in that they register a writer driver. This gives them a callback before the snapshot starts - a chance to flush transactions and hold off writing any more, for a second or two until the disk snapshot is created and block tracking has begun. Then they get a second callback saying they can resume.
More interesting is e.g. Hyper-V using this to snapshot the guest VMs.
It just takes you one step beyond being only crash-consistent, so that everything is actually application-consistent.
Implementing a VSS writer is a big 90's-style COM interface, but there is also a lightweight alternative model on top of that that eludes my search right now.
Red Hat has some similar convention for freeze/thaw scripts that can make API calls to the DB to ask it to do the same thing.