Hi, M. T. Search on "pull-ups" in Mamapedia recent posts and you'll find other moms with the same issue! Yes, the pull-ups must go and as others noted, he must become responsible for cleaning up all messes that result.
This is not fun for you; in fact it will be very stressful for a while, but if you can be absolutely consistent, you'll get there.
Have HIM throw all the pull-ups that remain into the trash can and put the lid on firmly. Praise him a lot for being a big kid, for saying goodbye to the pull-ups and for having the terrific new underwear you got him --- with his favorite character on it or whatever. (Have lots of extra underwear and extra sheets etc. ready in advance. Also be sure you have a couple of those waterproof mattress covers, one on the bed, one ready to go on when the other gets soiled.)
When he poops in his bed, you get him up; he helps strip the bed; he walks with you to the laundry room sink if you have one or the tub if you don't; and HE does at least some "washing" of the sheets. If you really want you can put plastic gloves on him since poop's involved..But I think if you just whisk the sheets away and you stick them into the washer, he does not get the full impact that HE must help clean the mess, so I'd have him do at least a few minutes of washing out the sheets somehow.
Then he has to wash himself up, maybe even have a shower in the middle of the day (many kids will quickly do anything to avoid bathing in the daytime so that alone may motivate him soon). Then he has to wipe up the floor where anything spilled, maybe even if anything didn't, but "just in case."
And he has to re-dress, which kids also often hate to take time out to do. Then he has to help make the bed. Let him do as much of that as possible even if it's not perfectly done.
He should figure out pretty fast that this is not only interrupting his sleep time; it's going to eat into his play time as well. You need to be calm with him throughout and not punish or yell: "I'm sorry but you're a big boy and big boys help clean up when there's a mess. I'm sorry this means there's less play time but you can play only when this is all done." Thank him for helping out -- always. Do be sure to go in and remove toys, once he's asleep, from the area where they could get soiled, especially toys that can't be washed.
As long as he's in pull-ups at any time, he will use them. If he's otherwise potty-trained he can do it; he may indeed be having some trouble, while sleeping, feeling his body's need to poop until it's too late. But the use of the pull-ups has meant he doesn't have to learn to feel the need in bed, and somehow his body's begun to associate being in bed and lying down with "time to poop" and it's OK because it doesn't even have to wake him and the pull-up takes care of everything.
You'll have a period of crankiness if he interrupts a lot of naps with the bed change, which is too bad, but if you reinforce using the toilet all other times with a lot of positives and rewards, at the same time you stick hard to the "clean up" routine every single time, he should get the idea.