Transactions don't have any knowledge about which block they will end up in. A transaction is basically valid forever. Of course there are reasons why it might not be valid anymore when it gets broadcast but that is only noticed when nodes try to execute it, such as:
1) The sending account has too little Ether
2) The contract you try to interact with has ...
Many bad things may happen, here is incomplete list of them:
Anybody may sign transactions/messages with your private keys as long as you unlock them
Anybody may use resources of your node to query blockchain state (some queries could be very CPU and HDD intensive)
Anybody may use resources of your node to publish large amounts of transactions, i.e. when ...