Huh? Big unsolved crimes receive unending fame.
That doesn't always work though - the crime may be something the public is aware of, and then the pressure to "close" the lead is even greater. There are numerous "big" crimes that the public has no awareness of though.
If the case is high profile enough, they will _always_ find someone to find guilty.
It seems statistically unavoidable that there are always going to be some big cases that go unsolved. It'll probably become less and less common - especially since it seems inevitable that nearly all DNA will eventually be traceable via genetic genealogy databases - but some crimes just won't result in any DNA or other significant evidence being left.
Or to make the crime legal by paying politicians