I don't know if there is a closet with random items in it where you work, but the last time I had a mishap like that (not split, but I spilled something on myself that was really obvious) I found some old sweater and tied it around my waist.

Stapler.

sneak out the back door and go home and come back. no one would notice my absence, around here. maybe ask a co-worker to cover if i were oncall.

What Pinky said. Surely there's some random sweater somewhere, if you don't have one of your own at work.

A big purse or bicycle messenger bag would also do the trick. Or wheeling yourself around in an office chair for the rest of the day.

i like lulu's suggestion - everyone needs to wheel around in an office chair more often. whenever my coworkers see me wheeling backward past my doorway to quickly fetch something while i'm on the phone, they laugh.

what did the hypothetical person end up doing?

I can't imagine how this could happen when one might have recently lost vast amounts (well maybe not VAST) of weight.
Nonetheless, I would stick an adhesive sanitary napkin to my ass, to deflect attention from the actual problem.

Sarong? Pareo? Lab coat? Choir robe? Trench coat?

Seriously, I'd probably take emergency measures (ie, duct tape), and run to the nearest Goodwill to buy a skirt.

Um, I think certain embarassment is inevitable.

Wear cute underwear?

Sweater or jacket around the waist and then a quick trip to Target. I try to wear jeans to work as much as possible--they have nice strong butt seams!

I would fashion myself some new pants (ala MacGyver) using coffee filters, some strands of hair and a piece of chewing gum.

This actually happened to me at my high school graduation. The many-decades-old dress I had gotten from my grandmother split up to my waist when I leaned over to pick up the shoe I had stepped out of. Mostly only the person proceeding behind me could see, and I don't even know if they did.

I held my diploma in front of my butt on the way out.