This past Monday my mommy and daddy went to eat, when they came back out daddy put it in reverse, then he backed up,then he put it into drive and it still backed, does that sound like the transmission giving out?
This 2005 Pontiac➖Sunfire had only 106,000 miles on it,and they bought brand new for $12,000.
it sounds like the shift linkage needs attention
When was the last time the transmission was properly serviced?
That,I do not know.
Knowing my mommy&daddy they think all there is to maintenance is oil changes &that's all,so probably never.
When your daddy shifts the Sunfire he's moving a cable that goes between the gear shifter and the transmission.
The cable moves a little lever on the transmission and that makes the car go in forward or reverse.
The cable looks like this:

Now you have to understand that the people who designed your daddy's 2005 Sunfire are mean GM executives.
They don't care about your daddy, or your mommy, or you.
They are bad, bad, men.
So to save money they used a cheap plastic part called a bushing on each end of that cable that connects your daddy's shifter and the transmission.
They knew those bushings would break someday but they didn't care.
The bushings look like this. The smaller one goes to your daddy's shifter and the larger one is on the transmission lever.

Well, they're made of cheap plastic and they wear out and even break over time.
The larger one that's on the transmission is more likely to go bad and if it breaks completely your daddy won't be able to shift gears at all.
So just remember, there's one of these on each end of the shifter cable. Your daddy may be able to fix this by replacing just the one on the transmission lever. That's usually the bad one.
They don't cost much. Under $10 and he can get them on Amazon, ebay, or his local auto parts store.

😆
I've never seen any brass bushing aftermarkets for it
.
That would be a permanent fix which GM should have used in the 1st place
.
I guess GM decided to designate this as a "wear part" and so do the aftermarket guys
