The game will allow you to bid on someone if you have the $ for the initial bid.

To get into such debt, you bid on multiple players when you only have enough $$ for them indivdually, and if you get them all *boom* debt...

or get in a bidding war.

The game does send a note "from the bank" warning you about low funds. The most expensive of your players will be sold if you do not get out of debt in 7 days.