BJ Penn entered the UFC as pretty much a strictly BJJ fighter, since then though the UFC has evolved and a fighter would need at least some kind of striking base even in the basics to survive. although Shinya Aoki has maintained a fairly decent career in Japan using pretty much strictly grappling but that is due to a phenomenal ability to utilize his BJJ from any position including some that he is forced to reduce to in order to get his opponent to the ground once he has somebody he needs to hold on and take it to the ground regardless of the position it leaves him in.
"If you get hit and it hurts hit him back you not knocked out yet."-Joe Doerksen
The Toxic Terrors (FFL)
Demetrious Johnson*Eduardo Dantas*Emanuel Newton*Will Brooks*Michael Page