Yes, you can get these fax machine to accept refills.
Theres a company that refills them, and tells you how to reset the machine to accept the chip.
Just google "faxjet 525 chip"
Im from the UK, and here we see Samsung M40 and M41 fax cartridges, exactly like this one.
You just refill the sponge and ignore the empty chamber if there is one.
I had this problem too, and pressing the button 4 times would clear it.
After a few weeks, though, the problem returned and couldnt be cleared.
Tried squeezing all the ink out of the sponge (messy!) but that didnt help.
Unfortunately, I just had to bin the printer then, so it was a bit of a...