(Community Wiki, since homework is off-topic for the site.)
As you hopefully know, the idea behind life insurance is that it pays up if you die early, while expecting most people to die "late". The decades of premiums from the many people who die "late" cover the benefits to the relatively few people who die early.
But retired people are going to die sooner than later; there's relatively not much time to accumulate much in premiums.
Given that, here's the kind of product I'd make:
- relatively low benefits,
- relatively high premiums,
- sell it as "building a nest egg for their grandchildren" or "not burdening their children with funeral costs",
- waiting period while premiums are collected, but before the benefits are eligible to be paid out,
- exclude many preexisting conditions,
- lots of fine print which prevent most people from gaining the full benefits.