Whenever you apply for citizenship, you automatically receive I-797 with 24-month extension on your GC expiration.
You'll be able to use your GC and extension letter to reenter the US, for example.
When it comes to employment, the best documents to use for I-9 verification are:
1) Valid driver's license or state ID
2) Unrestricted social security card. E.g. the one that doesn't say any conditions written on it such as "Valid for employment only with DHS authorization".
If you have such writing on SS card, get it replaced for free at SSA by filing SS-5 form. Never show employers your GC and or extension letters. They can't demand to see it (law gives you option to use List B+C documents for I-9). HR often don't know how to handle GCs and extension letters.