Keeping suede shoes clean is an arduous task in itself. Compounding that task with sticky substances only makes the job a bit harder. Many people would give up and either throw the shoes away or simply wear them with the gum, candy or whatever the sticky substance happens to be. Rest assured there is a method well worth trying for removing such sticky substances from suede shoes, and the success rate is fairly high.
The best way to start the cleaning process is to place the suede shoe in the freezer and leave it there until the sticky substance has frozen solid. The gum or other sticky matter may then be chipped away in pieces using fingers or the tip of a teaspoon. It might be necessary to refreeze the shoe if more of the sticky substance remains after scraping off the top layer.
Even after freezing and chipping, there will likely be some residue left on the suede shoe. A suede brush should be able to finish the job. Suede brushes are available at almost all shoe stores and can be found at mass retailers. Brushing the suede both with and against the grain of the suede will likely remove any additional residue from the sticky substance.
After removing the sticky substance, you should spray on some suede protector, which is available at most shoe stores, to help repel water and debris that may come into contact with your shoes.