I've had similar issues with thong or string style pieces. Though I currently don't have access to MD. I use the subscription version. I remember that anything smaller than 20 mm wide will slip into the mesh of the avatar in that area.
There are a couple ways to fix it, depending on your MD Version and if your using the supplied MD Avatars or imported Avatars.
The most resent version of MD added a feature that can smooth the avatar, basically subdivides the polys. Click on any part of the avatar in the 3D view, then look in the Properties pane. Avatar smoothing should be at the bottom. Though I'd be careful doing this, especially if you save as a Project. As it reloads the smoothed Avatar, but doesn't save the smoothed value in the Property Pane. Also may try adjusting the collision offset to the avatar.
It may also be a case of too much tension from the crotch area to the top of the back part of the bottom. Could try lengthening it a bit. Also if it's a single piece in the pattern window you can add an internal line and adjust the fold strength and degree. If it's a stitched (2 pieces) you can adjust the fold strength and degree with the Edit Sewing.
Sorry I can't be much help with the MD supplied Avatars, since I don't use them, and don't remember if the "cheeks" of the bottom actually collide.
I know that my imported Genesis 3 and 8 Models the glutes part of the mesh actually intersect causing some serious "Collision Confusion". the best way I found to fix that is before I export the model I use a morph that spreads them. Then I export it and create an Avatar with a more open space back there. It's not really realistic, I know, but it's the only fix I found to eliminate the "Collision Confusion". From what I've figured out is if the polys of the avatar are intersecting or even too close together (Sharp Bends) it causes problems.
Oh, just remembered, you can also try decreasing the Particle Distance of your Pattern as well. Decreasing the particle distance increases the poly count and sewing threads of the pattern, unfortunately this also increases the resources needed to simulate the Draping (or lack of in this case).
Hope this was helpful, without having my subscription on this is the best I can do from memory, which is not very good even on good days. lol 