I know about the dangers in online wallets, and how to use a cold - hot wallet.
The question could be formed like this:
If a swept address in an online wallet has 0 coins, and someone sends some coins there (some time later), will the coins be moved to the "web address" ?
the coins will not be moved to the new wallet...
If you have privatekey1 whose public key hash (commonly known as the "address") is 1address1, and you sweep privatekey1 into any other wallet, what happens is:
1) the "receiving" wallet will do a scan for any unspent outputs funding address1 AT THAT TIME
2) if it finds unspent outputs, it'll generate a new deposit address (it's possible the receiving wallet has a buffer of unused new deposit addresses). Let's call it 1addressfromnewwallet2
3) the receiving wallet will create a new transaction, spending all unspent outputs from step 1 and funding the new deposit address from step 2 (1addressfromnewwallet2)
4) the transaction from step 3 will be signed with privatekey1 (the key you're sweeping) and broadcasted.
5) since the receiving wallet has the private key whose public key hash is 1addressfromnewwallet2, it'll monitor this address for new unspent outputs, and it'll be able to spend those funds
If, after the initial sweep, somebody funds 1address1 again, those unspent outputs won't "magically" move to the address generated by the wallet you swept the coins in... You can, however, repeat the sweeping process as many times as you want...
There is a "variant"... If you import privatekey1 instead of sweeping it, both the original wallet as the new wallet start monitoring 1address1, in this case, for the untrained eye, it will look like the new funds magically "move" to the new wallet even after the intial import. However: since both the old and the new wallet have privatekey1, and they're both monitoring 1address1, both wallets are able to spend any unspent outputs funding 1address1. This might be a desirable feature in some usecases, or an undesired feature in other usecases!
