Bitcoin will die. Same with any other currency, if there's no one using it, there's no reason for it to exist.
With no one spending Bitcoins, there wouldn't be any transaction volume. With the no one trading on the market, Bitcoins will be worthless.
Bitcoin is more than just a currency tool. Nothing wrong with people just using Bitcoin for investment purposes or as store of value. In that regard, there won't be a time with no transactions unless Bitcoin becomes completely obsolete and people simply move on to something else. That's the exact reason why updates as Segwit and Lightning Network will get (or might get as the situation is still uncertain at this point) implemented. That's the beauty of Bitcoin's open source nature.