The only way I know for a stock to lose its stock symbol would be if the company was going bankrupt. If they were coming out of bankruptcy or if they choose to they can change their symbol.
As for “pink slip stocks” or “pink sheet” stocks these are simply stocks that do not meet the basic requirements of specific exchanges. Maybe they do not have a lot of volume or maybe they the stock’s price is too low. You can still trade them, but they will be bought over the counter not through a major exchange like the New York Stock Exchange.