I have a Norfolk Pine that the bottom has died off. I removed all of the dead growth, and the top is growing great; however, because there is no growth on the bottom, it is slightly top heavy and looks a little funny. I would really like to keep the plant, because it came from my grandma's funeral. Is there anyway to propagate this, or stimulate new growth?
Not really, no - that's normal for the lower branches to die off on indoor trees, nothing can be done about it. Giving it maximum light will help reduce further die-off rates.
Don't be discouraged in keeping the plant. I have a friend who has a massive norfolk pine inside. Very large and lush, with branching even. Perhaps it is asking for some certain care, and maybe if you can find what it needs, you'll be able to turn it into a healthier, impressive tree. I'd say go back to the basics: light, nutrients, soil, container size? Good luck with the plant. They're very pretty.
A lot of houseplant books do say that you can cut off and re-root the top of a NIP if necessary, but 1) I've never actually seen anybody try this and 2) I'd be hesitant to recommend attempting it with a plant that had a lot of sentimental value, for fear it might not work. They won't produce suckers, but if the bare stem at the base is bothering you, it might be possible to plant small NIPs in the soil around the trunk of the original plant: they could fill in the space around the bare trunk over time. And this is the best time of year to find small, relatively cheap NIPs.
If it were my plant, I'd do an air layering before I tried to do a cutting. But you should try to find data stating you can do that with this plant. Best of luck. And as stated above, and as many people would say, I'd think, you should make the final choice as to what is right. It is your plant. It is a risk, so I hope your plant turns out the healthiest.