What to do if a student claims to have turned in the homework but I could not find it?
Since you have no way to show that the student didn't submit the homework, it's simply your word against the word of the student.  Furthermore, there were lots of homework assignments from various students, so it would presumably be easier for you to forget receiving the homework than it would be for the student to mistakenly remember submitting the homework.  

If an unbiased third party considered this and assumed honesty from both sides, I think that they would conclude that it was more likely that you had lost/forgotten the paper than that the student had remembered submitting a paper when she, in fact, had not done so. 

If this happened with a student taking a class from a TA or faculty member under my supervision, I'd tell the TA or faculty member to "excuse the grade" and adopt a system for homework submission (e.g. use a learning management system) that provides independent confirmation that the homework was submitted.