Lower jaw pain

I have had major dental work done in the past year and a half, including having 7 teeth surgically removed due to severe breakage as a result of bruxism. While the majority of the teeth were molars, 1 upper lt incisior and 1 lt lower incisior were also removed. I was fitted for and currently wear a removable upper and lower metal partial.  A week ago I broke one of my last remaining molars (this one was mine not a crown), I broke in in half.
It is a left lower, rear molar, the one next to where the wisdom tooth would be....if left in the current state of not being removed, and an infection were to arise or an abcess (abscess),  is there any chance that it could cause any negative effects on my jaw.   I have heard it could disenigrate the bone tissue, causing breakage or worst case cause some sort of brain infection and maybe even death.    The only thing I suffer from is a constant pain in the jaw right now, Im taking ibuprofen for it.

[Jerome Tsang, DDS]

If its a breakage of a lower tooth, the more likely worse-care scenario is that it will spread down into the neck region and either cause a swelling there and compress your airway (which is life threatening) or it can travel down farther and infect the chest/heart region.  Both not pleasant results and should be addressed immediately.  

The brain infection is generally from an untreated upper tooth.

It can also potentiall remain in the jaw and disintegrate the bone inside weaking it and thus causing more likely breakage or even such extensive damage the jaw isn't save-able and must be removed.

Sorry to paint an ugly picture but it is ALWAYS best to address problems when they are starting rather than wait later.