I have a Kenmore heavyduty 80 series washer that will not do the spin cycle as of two days ago. I can still wash but it will drain leaving the clothes still wet. When it is supposed to be spinning I can hear the clicks and I can also hear the motor as if it should be spinning. The odd thing is I smell a burnt rubber smell while its washing especially during rinse and spin cycle. A few days ago I noticed small pieces of rusty metal or something like that appearing inside the washer. My Kenmore is very, very old. Has no serial numbers on it but on the inside lid it says Stylemaster 902202 sorry I know that's not enough. White body. Control panel is brown/black with silver knobs. I'm still trying to find out what model/serial number it is. But should I still wash even though I smell that rubber smell??

The burning smell is the drive belt. The transmission is probably locked up from old age and this will cause the belt to smoke/burn since the motor is just spinning and the transmission is not moving. You could try to replace the belt BUT with a old Sears/kenmore/Whirlpool unit it is probably a bad transmission.