Can you owe a player in monopoly
You must do everything in your power as the debtor to pay off the debt 


Count your cash
Sell houses 
Mortgage properties


If you then still don't have enough you can ask other players to buy the mortgaged properties from you to raise enough cash.  This could come from the person you owe money to.  Otherwise, you are declared bankrupt.

In practical terms, not many players want to continue playing with no money and wholly mortgaged properties, therefore usually bankruptcy is the best option.