Nomenclature for deterministic algorithms that might fail What do you call an algorithm which is


Deterministic
When an answer is returned, it is correct
For some input, the algorithm returns no answer (fails, in bounded time).


Such algorithms crop up a lot in cryptographic attacks, for instance, where a
cipher is deemed broken when an attack (provably or demonstrably) works "most
of the time".

I'm working in a different field (coding theory) with an algorithm of the above kind. For
random, uniformly distributed input, the probability that the algorithm fails
seems to be so low that in practice it can be more or less ignored. However, we
have no succinct characterisation of input which cause failure. Previous work on
this algorithm has called it "a probabilistic algorithm" but I find this an
abuse of the term, since the algorithm is deterministic, once the input is
known.
I do not have an authorative answer but two proposals.

Such algorithms compute partial functions, so you could call them partial or partially correct algorithms.

Working off your literature, the class of algorithms you defined is that of Las Vegas algorithms. Even though the implication  is that the algorithm is randomised it certainly need not be; even though you have access to random bits you don't have to use them.
If you want to stress determinism, you can use deterministic Las Vegas algorithm.