It's impossible to send them to an invalid address, BUT it's entirely possible to send them to an address for which no one has the key.
Take for example: 1BitcoinEaterAddressDontSendf59kuE
Check it out on blockchain. If you can brute force the private key, the coins are yours. Is it impossible? Theoretically, no, but practically...
Let's say you had a super computer that was guessing 999 trillion keys per second. It would take you 3.5 billion years to exhaust just 10% of the keyspace, which means in 3.5 billion years you would have a 10% chance of having guessed the key. Good luck with those odds!
Watch that address. If you see someone spending its outputs, it is probably time to get out of bitcoin.
How do people know somebody doesn't have the private key to that address all along and they're just sitting on the coins?