My rudder post was slipping inside the rudder so I had it rebuild professionally. I DO know what they did though. In my case, the rudder was solid fiberglass - very heavily built, given its vintage: 1972 Hughes/Northstar 38.
The boatyard ground away the leading edge of the rudder to expose the rudder stock and the splines that run aft from welds on the stock into the blade of the rudder...buried in the fiberglass. The slop in the rudder was caused by failure of these weld points. They rewelded, glassed, fared and reinstalled the rudder at a cost of about $3K.
I've also heard on newer boats, rudders are not solid fiberglass, but foam filled. In these cases, repair requires you split the rudder open like a clam shell. I do not have details on this procedure but have seen this explained online. Goolge may yield some results.