If you have a sequence that's neutrally mutating with no corrective pressure it won't eventually disappear. At most it'll mutate into something unrecognizable [^1]
For example, your genome is littered with pseudogenes. These are mutated, ineffective shadows of what used to be a functioning gene. Nonetheless they're still close enough to what they used to be that you could reason about them in an evolutionary sense, eg: this one is also a pseudogene in other primates (i.e. it stopped mattering a long time ago), or this other one has a functioning homolog in non-primate vertebrates (i.e. it kept functioning in that lineage).
[^1] as a first order approximation. There are of course other structural events that can create much more change per event than your run of the mill single-point mutations that occur during every DNA replication.