If the subpoena is served while she is director, resigning should have no affect of the powers of the House to require her to testify.
The subpoena is for while she was/is director.
Resigning does Not absolve one crimes they have or may have committed.
We have seen this situation before. People have been issued subpoenas to federal employees to testify. Those people resigned or retired and the courts quashed the subpoenas.
You are making a classic mistake of projecting what you wish the law says rather than what is says. That is what Socialists and Communists routinely do. I am not saying you are a Socialist or a Communist, just that you are doing what they do.
When she resigns, she will turn in her cell phone and other records. If she shows up for a hearing, she will simply say, “I can’t remember. I do not have access to the records I would need to answer that question fully and correctly.” I will be up to the House and Senate committees then to subpoena those records.