Goes out of round-agitator?

While taking my 1993 Kenmore 70 series washing machine apart to find and determine if the motor coupler needs replacing (it does!), I noticed a round rubber piece at the base of the agitator that seems to no longer be in place. For the last 4 years the washing machine has gone out of balance quite often.  Could this be the problem?  If so, how do I access this rubber piece from where I am now (the motor and water pump are off) to replace it? Do you know the proper name for this piece (I'm not sure if the old one will still work)?
Thanks!
Candace