When my back right brake caliper fell apart I replaced it but now my brake pedal goes to the floor when I start the car but will pump up and will be fine until you wait a few seconds then it's soft agian I bleed the brakes in all possible ways and my abs light is not on so I never messed with the abs pump and I don't think it's a brake booster internal leak but at this point I need help and suggestions. (Ps yes the brakes worked fine before I just didn't change the brake pad soon enough because I bought the car from a auction)

 

First, it does still sound like there is air in the brake lines as that is the typical symptom of pumping up the brakes and then they bleed off.

* I am a bit confused, did you replace the rear wheel cylinder as with drum brakes or does this car really have disk brakes in the rear? Are you sure that you have ABS or did you just see a place on the dash that says ABS? The Lx should have drum brakes and no ABS.

**Assuming that you blead after you replaced the wheel cylinder, as a new part does not come pre blead.

*A quick google search will show proper brake bleeding procedure. You are supposed to start with the furthest brake from the master cylinder. ensure that you do not run low on brake fluid as it is easy to get air in the lines if it runs low.
I have heard stories of people getting new wheel cylinder or calipers and having a spot where it internally holds air and is difficult to get the pocket of air out but I have never experienced this.

*You can use the two person brake bleeding system, but if there is no real issue with brake lines (clogged with rust) etc, I just use a mighty vac pump ($40ish) and do the work my self. I have tried the cheaper $20 harbor freight vac pumps and they don't work very well.If you re-do the brake bleeding, I would get a large bottle of fluid and vacuum the fluid out until it looks clean, not just until you don't think that there is any air in the lines.

*If there is no way that the issue is air in the line, consider if the wheel cylinder that you replaced is bad. If it had been sitting on the shelf for a long time, it may have dry internal seals or if it was honed too much and now the seals can't hold pressure (cheap remand parts)
*Second i would look into the master cylinder. It should not pump up and hold if the MC is bad, it could still pump up, but should slowly bleed off. Often with an old MC, if you push fluid back through the MC from a caliper/wheel cylinder, this can ruin the MC. For this reason, when i change fluid and put on new pads/shoes, I always loosen the bleeder nipple and use a hose to catch the fluid to save the MC. If you replace the MC, bench bleed it so that you don't pump more air into the system.
*Third, some people have said that they get bad rubber lines and when you press the brake pedal, they expand and you have poor peddle pressure. I have never seen this personally.

*Fourth, if you do really have ABS, I have heard that you can get air stuck in the distribution block (where all the lines meet under the hood in an aluminum looking squarish block). This can be difficult to get the air out of. Look to see if there is a bleeder nipple on this block, but I would do this as a last resort. There may also be a way to make it self bleed or vibrate to remove bubbles via some key off on combination. I would not know if there is.

**New brake fluid can make old parts go bad. MC, caliper and wheel cylinder.

 

I have rear disk brakes and I do have abs the pump is on the passenger side next to the intake and the pistons for the rear caliper fell out when I removed the caliper and all the fluid for that caliper came out and it had to sit over night like that cause it was 9pm at night and I couldn't think of anyway to fix it but I'll try and jump the abs pump to kick on and try and see if any air comes out then but if I pump the brakes it hold the pressure I put a brick on it all night and it held the pressure but if I take my foot out and let it sit it goes right back to the floor