Got rejected from my dream company on Monday after making it to the final on site interview. Is it too late to send a thank you (rejection) email to the recruiter?

Pretty sure I lost the job to a better candidate because I did well during the on site interview. She called me and told me the bad news so when she asked if I had any questions I was still in shock and couldn’t utter a word. Now that I’ve had time to think about what happened, is it too late to send the recruiter a thank you email and asking if she will keep me in mind if other opportunities come up? Or is it too late to send this email out two days after being rejected? I’ve heard of stories where recruiters call back people who have interviewed before about new positions or when the person they chose for the position backed out and they called back the 2nd or 3rd choice.

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