My wife is elegible to enroll in Cobra since I was terminated/Job Elimination due to work being moved out of USA. I am on Medicare so this question is about her continued coverage after Cobra Coverage. If she decides to go with the same company after going off Cobra, how does Pe-Existing Condition play into this scenario? 
Does the Insurance Company have to accept her when she applies for a Single Policy regardless if she does in fact have a Pre-Existing Condition? The same insurance company covers her under Cobra as was covering her when I was employed. Thanks for your assistance.

If she converts her policy, they should not use pre existing conditions against her. My wife was with Kaiser on COBRA and they automatically switched her over to a regular plan. Of course, and she had several minor health issues. If she's individually underwritten, it will come down to how costly her health condition is to the insurance company.

Fred:

We were with Anthem under my group policy until my job was zapped. I am 65 so I just went ahead and of course got on Medicare/Medicaid. I am elegible for Cobra coverage for 18 months but after that we of course must get a individual policy for my wife. She does have some health issues so I guess of course her rates will be in accordance with how serious her health issues are considered.

Robert:

If your wife has health issues, they won't increase her premiums, they will either insure her under the federal or state statutes, or decline her.

The people with serious pre existing conditions do not pay enough to cover their medical expenses, the healthy people that don't use their coverage compensate.

convert your COBRA coverage

At the end of the COBRA period, convert it to an individual health insurance policy under the health plan rules and HIPAA.