I kept some non-filtered grease having used a large electric griddle - from a big project requiring 6# of bacon. Some went in the freezer. After about 5 months the tub in the in the FRIDGE, in a tight sealing quality tupperware thingie, ...I took it out yesterday and in fact it IS growing a couple green spots about the size of a dime. So it can go rancid for sure.
I'm in the medical field and the "strain the grease thru cheesecloth or paper towel using a sieve" makes a lot of sense! I had not thought about this till now.
The itty bitty chunks of FAT and especially the tiny bits of MEAT are still having some metabolic activity to the very end, and the high prolonged temps cease living cellular activity. Then, as meat does everywhere in nature as it tries to dissolve and liquify in the final stages of cellular breakdown, it releases things that are conducive to bacterial growth. Unless you burn something to carbon, it still has cellular breakdown activity and potential for another cell to use that media for growth. With that, I would recommend warming your oil for higher viscosity so it passes through the paper towels or cheesecloth more easily. Be patient. High quality paper towels might be too restrictive. Let it sit and drip - and the filtered oil should be usable and safe a good bit longer than unfiltered.
Now the oils. These are saturated and unsaturated oil "acids". (Polly Unsaturated Fatty ACIDS or PUFA on the label of cooking oil.) Tis a mild acid, but molecular acid never-the-less. Thus when properly strained with care, and stored in a quality container with an excellent seal to limit fresh O2 exposure which oxidizes, it could very well remain viable for a heck of a long time in a cold fridge. On THAT, my Southern brothers and sisters are probably correct! The South may rise again!!! :)