We do not have a feature designed specifically for this, but you can track who you loan cat traps to in Shelterluv a couple different ways.
If you create a custom people attribute (How do I use attributes on people records?) called something like "Borrowing a Cat Trap," you would be able to easily add this attribute and quickly remove it from the attributes tab in each person's record.
You would also be able to filter for people with the attribute from the people tab on the main page to see who has a cat trap.
You can also use a custom memo type (which would not sortable from the main people page) to indicate more details about the trap that has been loaned out, such as the trap number(s) or the type of trap.