My mom has a green card that expires 2028 but has been out of the US in the UK for over a year due to COVID travel restrictions. Can she enter now?
Assuming she doesn't have a valid Re-entry Permit, she technically doesn't have one of the accepted documents for entry of a returning immigrant, as listed in 8 CFR 211.1(a). A green card is not one of the accepted documents after an absence of more than 1 year, and she doesn't have any of the other documents, like a Re-entry Permit or an immigrant visa.
However, under 8 CFR 211.1(b)(3) and 8 CFR 211.4, the immigration officers at the port of entry have the authority to waive her failure to meet the documentary requirements, if they determine that she has not abandoned residence. They often will grant the waiver if it's the first time, the absence is not too much over a year, and/or there is a good reason for not returning earlier (e.g. COVID-19). So if she manages to make it to a US port of entry, there is a good chance they will just let her in, perhaps with a warning.
The officer could deny her entry, and pressure her to voluntarily sign I-407 to relinquish her permanent residency. This is voluntary, and she can refuse. If she refuses, they will give her a Notice to Appear for removal proceedings in immigration court at a later date. There, she will be able to present her case to the immigration judge, and if the immigration judge determines that she has not abandoned residence, the immigration judge can grant the waiver for her failure to meet the documentary requirements (think of it as a second opinion on the immigration officer's decision).
The other option to all this is that she can apply for an SB1 returning resident visa at a US consulate (which will meet the documentary requirements since it is an immigrant visa). However, this requires showing that she could not return any earlier due to circumstances beyond her control (which may be harder to prove than showing that she did not abandon residence). Also, there is no appeal for visa denials.