A crappy meme, much like a gene that causes lethality or other problems, will become extinct.
Natural selection isn't predicated on the removal of genes which have adverse effects. It is more of a positive feedback system. You don't want genes to go extinct, as that limits variation. Because genes interact with their environment, although a gene might be undeniably harmful to its carrier, in another situation it could become useful - it could even preserve the entire species. There's really no such thing as a "crappy gene" (I know you said crappy meme, but you are expanding on the connection between memes and genes).
So it's more accurate to say that a meme which is less likely to inspire replication/reproduction will be overshadowed by more popular memes. It doesn't make it crappy, necessarily, it just means it has its limits.
One of the most unimaginative and dull memes, in my opinion, is "keep calm and carry on". Yet it is actually one of the most popular (and profitable) memes. Within an unimaginative and dull section of the populace, it has found its niche.