You have to remember that incontinence is a symptom caused by something else. For example, stress incontinence is usually caused by weak sphincter muscles, typically women that have had children can get it. It means every time you place stress on your lower abdomen (coughing, sneezing, laughing, etc.), you can have a small amount of leakage. By "full blown incontinence", I assume you mean a lot of leakage no matter what. However, that would only happen if your sphincter muscles were completely trashed - wiped out (or your incontinence was from another source - like urge incontinence stemming from your bladder muscles and nerves themselves). There are diseases that could cause that to happen. If you suspect something like that then I would highly recommend seeing a doctor.
From what i've read during the years on medical articles and post in incontinence message boards, stress incontinence can worsen to full blown incontinence but like diaper degraw said before it's not very common. Stress incontinence is triggered by other bodily "faults" than for example urge incontinence.
If you want to know more please let us now or ask your urologist
There's really no reason why it can't develop into that. Incontinence, disregarding the source, is your muscles weakening and unable to hold back either your urine or poop.
So it makes perfect sense that, if you're incontinent long enough, that your muscles have significantly weakened and therefor are untrained. Even if your stress is gone, your muscles are now weak from not being used in so long.
I'd imagine that would take a long time to happen though. And this is all my assumption, but it makes perfect sense.
Even with stress incontinence, the muscles are being used all the time, they just aren't strong enough to hold back under extreme pressure. Normal contractions of the bladder won't cause leakage until it gets severe. It can become full-blown, but not caused from the stress incontinence itself, unless the sphincter is completely non-functional. In that case, urge incontinence would likely develop as well.
(I don't assume the original question was relating to bowel continence.)
Whatever is causing the muscles to become weaker is the main factor of if it will progress any further over time.