The latch string is always out old-fashioned phrase spoken informal
You are always welcome to visit.
Please come and visit us again. The latch string is always out.
You can come to us whenever you are depressed. The latch string is always out.
To visit
Go somewhere for a brief visit or purpose
To be no longer welcome to stay in a particular place because one has remained a guest for too long, or done something that makes others feel bothered or annoyed
A short visit
to offer someone to visit your house for doing something.