What if the winner didn't claim the key for over 7 days?

Then you send in a support ticket and ask for a reroll. :)
If they've been online during that time, however, they may have seen the key, so you may want to check their steam profile to see if they've activated.

I usually like to leave them a message on an old GA of theirs or their Steam profile to let them know they have a win waiting first ...

Reroll, if you are sure the key is unused.

I've had a similar situation some time ago. The winner marked the key as "received", but didn't claim it. I've sent a support ticket with "Not Activating Won Gift" reason & the user was suspended for a few weeks. I didn't ask for a reroll as I don't know if the key I gave him is still valid.

poke them :3

You know what to do.

View attached image.

Ill try to chase him up 1st.