Good question! If you owe $50,000, why would your creditors accept a deal where you only pay, say, $20,000? The answer is simple: the people you owe money to would rather receive something than nothing.
Here's the same question, asked another way: what happens to your creditors if they reject your proposal? If they don't take the deal, your only other option may be to declare personal bankruptcy. If that happens, they will most likely get less, perhaps a lot less, than you offered in the proposal.
So, for the creditors, accepting your proposal is their best options for collecting the most money possible.
Also a good question. If the creditors accept my proposal because I am offering to pay them more than if I went bankrupt, does that not also mean a proposal costs me more than if I went bankrupt? The answer, in most cases, is "yes". If you offer your creditors less than they would receive in a bankruptcy, they have no reason to accept your proposal; they would prefer that you go bankrupt.
However, a proposal may still be your best option, for a number of reasons.
First, you are avoiding bankruptcy. That's an excellent reason for filing a proposal.
Second, with a proposal you have certainty. You know exactly what you are required to pay each month.
Finally, with a proposal you are allowed to keep your assets, such as your house, which you may lose in a bankruptcy.