On the Wikipedia page about cache replacement policies, there is a small section about LIFO/FILO policy:
Last in first out (LIFO) or First in last out (FILO)
Using this algorithm the cache behaves in the same way as a stack and opposite way as a FIFO queue. The cache evicts the block added most recently first without any regard to how often or how many times it was accessed before.
I tried to look a bit for an application of this policy but didn't find any example. In my opinion if you discard the most recently added entry, then it defeats the purpose of caching. When there is a cache miss, you'll fetch the data, save it in the cache but it will likely be the first one discarded on the next cache miss, so why did we cache it at all? The only reason I see is that each entry will be likely fetched only one, but then why implement caching then?