Theoretically, there is an almost (I say Almost because of certain real issues) of a real world equivalent:

The Dead Sea.

This is not so much a true sea, but rather a a high saline content lake that sits 1,378 feet below sea level. As a result, it could have a river flowing from the real Sea into it, but eventually without some mechanism for the inflow to leave, it would eventually fill.

In a fantasy world this could be accomplished by either extra diemensional rifts, portals, undergound sea etc.