Can I be given extra duty 14 days from being separated by the army?

They can up to the minute you sign out !

You're going to have to explain your question because the way you've worded it doesn't make any sense

Until you’re out of the Army you’re still under your units command

Sounds like you got an Article 15 but without more information to go on no one's going to be able to assist you further. If it is an Article 15, then yes they can.

Unless you are getting out on a medical, it looks like you either didn't do what you are supposed to do or you are a fuck up. I never knew anyone who left the Army as a PVT unless they were chaptered on a medical or were a complete fuck up who lost rank because they were as fucked up as a football bat.
As for the extra duty, hell yes they can and will. Hell, they are probably looking for reasons to give you more. This stupid ass question is a good reason because you gotta know that they already know you came here and showed your ass to the world. The Army is a small world and everyone knows someone who knows someone who knows you. Your best bet is to shut the fuck up, do you ED and hope they don't try to find a reason to send you off with a chicken dinner. (assuming you aren't already reserved a spot at the table.)

And, if your feelings are hurt by the honest answers you got here, too damned bad. Come here and ask stupid questions and you are going to get brutally honest answers.

You sure are eligible for any and all extra duty as corporal punishment right up to your discharge/rotation day.

Yes. A sailor in a command I was attached to was within one week of separation and thought it was a good idea to tie a bunch of his uniforms together and drag them around base from the bumper of his truck. Don't know the exact reg, but he was put on legal hold and was sent to Captain's Mast and did not separate when he was expecting.

Two weeks, 1-day, a few months... No time period forbids a command from awarding extra duty if applied in a fully legal manner.

What have you done that makes you ask this question? I love a good story.

Ummm.... Yes they can and I've seen it happen! I knew a man who was out processing, just a week out from going on terminal leave. They put everything on hold so he could receive a field grade Article 15, demoted from E4 to E1 but that wasn't all. He was then separated from the Army under Chapter 14, administrative discharge for misconduct instead of the honorable discharge he would have gotten otherwise. What did he do? They got him for dereliction of duty, disobeying orders and lying to his chain of command. All he had to do was knuckle down and do his job for what little time he had left. This may not be the answer you're looking for but don't be an idiot!

Yes. They crashed a DC8 or whatever just as I was sposed to come home from Germany. Extended me 2 wks "for the convenience of govt." Dunno what I was so pissed off about- all it was, was a 2 wk paid no duty vacation. (When I look back its lucky they didn't extend me about 5 yrs in mannheim haha.) Sure I'd marked the day on a calendar for a year and had things planned stateside with family, but- hell yes they can. Been there, done that. Came back on a C 141.