What would cause my washing machine to stop at the rinse cycle and smell?
It sounds and smells like the pump that purges the water from the tank has failed. This could be due to bad windings on the motor, motor damaged due to excessive surges on the power line (perhaps lightening while the washer was running) or some object getting down into the pump and jamming it up so the motor overheats. 

If the tank drains normally after the unit has been allowed to cool down then the problem may be in the timer unit that sequences the wash / rinse cycles. These timer units (particularly on older units before everything went electronic) also have a low power motor that can burn out.

The timing sequence controller in a washer also controls relay contacts and high power switch contacts that turn the motors and pumps on and off. Sometimes these contacts go bad and start to spark and burn. It is possible for the contacts to weld together and prevent the proper sequencing of the timer past a certain point in the cycle. 

In either case of the issues involving the timer it usually requires replacement of the timer unit. This can get relatively expensive to repair so it is worthwhile to evaluate the age and condition of your existing unit so you can make an intellegent choice between repair and replacement of the unit.