Inviting correction by people with more extensive engineering experience; most of mine is in breaking rather than building.
A synchronious replication of a VM would be an example of a FT service (so it can continue to work without losing the current state). Failover is a process of restoring the operation with losing the current state (so vmware's HA is clearly FO if you dig below the marketing bullshit).
Described behaviour of the Task Manager is not FT, FO or HA.
Other commenters provided good variants, personally I would go with "Graceful Degradation", because it proceeds with a minimal functionality only if there were problems with normal operation.
Adjusting the introductory statement on that Mozilla page we could arrive at something like:
"Progressive enhancement is a design philosophy that provides a baseline of essential content and functionality to as many users as possible, while delivering the best possible experience only to users" ...whose computers have sufficient resources such as RAM and CPU cycles available to process and display it.
[1] https://developer.mozilla.org/en-US/docs/Glossary/Progressiv...