Do you send a thank you to someone who came but did not give a gift?

For my own peace of mind I would thank them. You do not always receive a gift in a package with a name on it. It could have been a cash gift. It could have been another contribution. I would "thank" them kindly for their attendance and contribution to your happiness.

If I was you I would cause they thought of you and coming they show that they care about you

I would send a thank you also. It is just a polite thing to do and who knows, maybe their card got unattached from the gift or something like that. I once went to wedding where the gift attendants took all the cards off the gifts and placed the cards separate. The bride and groom did not who gave what!