Passive BLE is a thing that's in active development (meaning it wouldn't require a power source) – this has the potential to work, but the range would likely be extremely limited. Inches, not feet.
The right design would have the ability to reply to another device with an advertising beacon, which could work in a limited set of circumstances, with some tweaks to how the AirTag protocol currently works. Like, if you stuck your wallet in your pocket next to your phone or on a table next to your laptop.
RF ambient energy harvesters also exist, which use more generalized RF to gather energy in a generic way. Where RFID sends the signal intentionally that powers the RFID reply beacon, you could theoretically find something in the ISM that gives you enough power to somewhat reliably harvest that instead.
https://www.digikey.com/en/articles/rf-energy-harvesting-bat...
Not sure about the advertising beacon interval but if it's flexible enough you might be able to join the two concepts. The limitation is likely figuring out the right ISM band, and the right package (coil size) to harvest enough energy reliably to send out your advertising beacons.
Distance and directionality (phase) once again affects energy output, but also, you would need to build a coil to a specific size to the frequency you're trying to harvest. Not sure these ever match up for this application. Higher frequencies would allow for smaller coils, but with lower power output efficiency.
The math behind this is wrapped up in the definition of the Q factor, and this is very similar to how you understand radio propagation in general, if you're looking for something to research further.
But, my ELI5 to myself: BLE beacons are already using ISM, so if your goal is to retransmit an ISM signal that beats the noise floor you're using to harvest RF in the same range, efficiency is going to have to be phenomenal in your system design (or take advantage of some power differential).
There's been some interesting projects and papers on this in the last 10 years or so, and the UW had an interesting retransmission concept a year or two ago they built. Links appear to be broken now though.