Once everybody sends their coins to xapo and nobody withdraws BTC from xapo we are not going to have any transactions.
Mining will continue as you can mine even if there is nobody sending and receiving coins.
Miners will keep on getting their block reward, until this also dries up and then the whole chain might be supported by hobbyists.
Xapo will become some kind of Paypal and Bitcoin....will probably die.
Are you sure that if there are no on chain transactions, then miners can still mine the Bitcoins and get the reward. Because I think mining is basically the verification of the transactions. If there is no on chain transactions, then how can mining be possible?
yes they can. a bitcoin block can be valid as long as it has at least one transaction and that one transaction is the coinbase tx which is giving the founder of the block the block reward plus fees. there is nothing forcing a miner to include any additional transactions in that block, only an incentive to get the fees.
if you check the blocks that are found every day you sometimes see these "empty" blocks right now. of course the reason for them is different (for example spy mining). or you can simply check the early blocks (anything below 100) to see empty blocks.
example:
Block #511512
https://blockchain.info/block/0000000000000000000d637d922588b7d30c85fd35d87b42ef86a8ce9609764eBlock #10
https://blockchain.info/block/000000002c05cc2e78923c34df87fd108b22221ac6076c18f3ade378a4d915e9