An abbreviation for 'pay my department' is very narrow and I cannot see that anyone would want to register a domain about it.
As for the other possible meaning, I'm not a great fan of typo domains in general. Putting that aside I would not assume that 'dept' is a very common typo for 'debt' either (?), but I'm not a native English speaker. In addition, paymydebt.com is parked. It would have been better for parking of a typo domain if the main domain was a fully operational site which had some traffic.