Once they have exhausted FMLA they can be put on COBRA.  

It does not depend on the "situation" once they have exhausted protective leave you can COBRA them.   I have put staff on STD on COBRA as they were not covered under FMLA.  You are not terminating them, which is where the confusion might be coming from.  When to terminate is a company decision, if an employee is on STD/LTD and not on FMLA.  Most legal counsel will tell you to carry them 12 weeks as an employee weather on FMLA or not but you can COBRA under 12 weeks if they are not covered under FMLA.  

When an employee is on LTD is a company choice on weather to term or not, can you afford not to replace the person, depending on the situation.  Their coverage will on LTD will not stop if they are terminated.

Our BPA agreement with our medical insurer dictates how long someone may be carried on insurance.  It is typically 6 mos from the beginning date of disability.  Once someone reaches that point, we send them the Cobra information.  We don't term them until they have been on disability for 12 months and before we do, we also conduct an interatctive ADA discussion with employee and his/her doctor.

At our company, their active medical coverage is tied directly to their active employment.  Medical coverage is terminated when their employment is terminated - and of course at that time they become COBRA eligible.  If they are just out on leave - or out on LTD, but their employment has not been terminated - we continue their coverage but request they continue to pay the "employee" portion of their benefits.  They have to mail in a check every two weeks, but of course this is all in writing prior to them going out on an unpaid leave of absence.