What is the risk of not replacing an extracted tooth with an implant?

A dental Implant is a great idea before you begin treatment.  Find a surgeon who s doing immediate placement implants.  The tooth is removed, the implant placed and the bone graft is down at the same time.  There are even fast integrating implants that heal in 2 months!!!  If time is your issue, there are solutions.  You could start the osto meds sooner with the newer technologies.

You do not have any problem setting an implant , actually its better for you , that way you will preserve the bone height on that area , and this will benefit also the contiguous teeth . There are several techniques to work this out. Hope this helps.

We know that only a healthy tooth or a dental implant will maintain jaw bone dimensions which will atrophy (shrink) after tooth loss.  However looking at the bigger picture in your case one isolated lower second molar is not a significant tooth to replace with an implant in the presence of significant systemic disease.  Controlling your osteoporosis and keeping cancer risk lower is your main medical concern and you will likely be taking bisphosphonate medication soon in addition to your current prescription.  This helpfully interferes with bone metabolism in osteoporosis sufferers but can lead to complications with bone and implant healing and nasty bone healigng side effects that are difficult to treat.  I would be very cautious about putting your missing molar ahead of your serious medical issues and my advice would be to concentrate on the osteoporosis and cancer treatment as a priority.  You will not notice any loss of dental function from your one missing tooth and it is not a visible tooth when smiling.