Disclaimer: I work for Frontier and have a working understanding of the fiber gear we deploy and how it works, but can’t provide definitive policy guidance on how to deal with ‘left-in-place’ equipment, all of which is the property of Frontier.
TL;DR for dealing with the remainders of a disused installation
I’d suggest removing any PSU/BBU equipment and leaving the ONT. If you must remove the ONT, I’d suggest leaving any slack on the fiber drop coiled up and out of the way or otherwise serviceable. There may be some IR light coming out of the drop if it’s still connected at the hub (they are generally left connected) that’s mildly hazardous if you look right at the end at close distance so I’d cover up the end of the drop somehow.
Longer contemplation of the subject
Frontier (formerly Verizon) FiOS has used a variety of vendors and models of equipment at the subscriber premises. Originally there were 3 elements - power supply unit (PSU), battery backup unit (BBU), Optical Network Terminal (ONT) - all necessary Because Reasons™ the BBU performed critical voltage conversion from the PSU. More recent gear had the PSU and BBU functions integrated into one unit. And the most recent gear tends to omit the BBU altogether, with a +12V aux input if you’re inclined to provide alternative power should mains go down.
The BBU also performed varying functions depending on the make and model. Some would run everything for a period of time then drop to just supplying POTS (phone service). Others would run the whole show until the battery reached the ~40% mark then shut off until the subscriber hit the ‘override’ switch and run everything until the battery was exhausted.
If you don’t have FiOS service any more and you’ve cleared any contractual obligations with Frontier, I don’t see why you can’t remove any lingering BBU and PSU - even if you think you might want FiOS service again. The company would of course like for you to leave any old ONTs intact since that would make for simpler turn-up if you ever subscribe again and will have even stronger feelings about leaving the fiber drop in serviceable condition. But the reality is that new installs are seeing new-architecture ONTs that are comparable to a home broadband router that cost a fraction of what the old pizza box-sized ONTs did, and ‘re-activation’ installs are generally budgeted the same amount of time for the tech doing the inside work as fresh installs. If everything absolutely must go I’d plead to at least leave the fiber drop reasonably intact (coiled up somewhere not kinked, end covered so that any slightly-hazardous-to-the-eye IR light that might be coming out is blocked).
Exterior old-school installation. The box to the left used to contain an ONT - now it’s a slack tray for the fiber drop and jumpers POTS from the ONT inside to the original copper NID between the ONT and the power meter
Washed-out photo of a ‘modern’ interior ONT install. Upper left unit is the PSU. Right unit is a (now-disused) RFoG device that decodes the 1550nm linear video signal and transmits RF for cable TV service. Lower left unit is the ONT itself; the fiber drop (white cable with green connector) comes in from the slack tray outside. I have a UPS powering the ONT so I should see hours of uptime in the event of a power outage.