Sometimes I show up at an address and discover my subject moved away "a couple months ago" or something.
When I miss somebody by such a short period, I often find their new info isn't showing in the proprietary databases yet. But one place it could appear immediately is in the U.S. Postal Service's address forwarding files. Many people request the post office to forward mail when they move. The USPS forwards mail for up to 12 months.
I could complete a Request for Change of Address or Boxholder, etc. form, send it to the post office serving that neighborhood and wait weeks or months for a reply, if they reply at all, or I could inquire less directly by sending a "RETURN SERVICE REQUESTED" envelope to my subject's last known address.
The caveat here is, I'm not getting a formally stamped response from the USPS to an inquiry that includes all the court case information, which may be useful in court if a defendant is trying to evade process service.
But for simply finding out where somebody may be staying or at least picking up mail, whether it's related to a court case or not, this is something you can do for the cost of a stamp and envelope and a few weeks' patience.
Prepare an envelope to their last known residence, addressed like this:
The key term here is "RETURN SERVICE REQUESTED." Place it under the sender's name and address. This tells the postal service you'd like the envelope returned if it can't be delivered as addressed, with the new address or other explanation for non-delivery.
If the person is forwarding mail, you'll get a return within a few weeks, or even a few days, like this:
The yellow label on the bottom shows their new address. If you get nothing back after a month, they probably didn't request mail forwarding.
By this time I would check in with the proprietary database records again. However if you don't have access to those sources, consider consulting with a licensed private investigator.