It is possible to sell a home that has been eaten up with termites. However, you would need to have it treated before you can put it up for sale. You can get a termite inspection done and then have it treated as this is the best option. This may end up having a negative impact on the resale value as it may reduce it.
You can definitely sell a home that's been eaten up by termites as long as you disclose this fact. The buyer will either have you pay for an exterminator of the buyer's choice or deduct the money from your portion of the sale. Depending upon where you live, failure to be honest can be met with penalties & fines up to 5 times what it would have cost to fix and ruined character on your part.