How do companies who must market unpopular things (i.e. funeral services and medical equipment) survive?

You are really asking about selling these two examples, not marketing them.  The marketing plan would include advertising, media placement, etc.

Don't assume that because a product doesn't have sizzle or sex appeal that it is unpopular.  You gave two very different examples, but the answer holds true for both of them -- they both provide a very necessary service.  The sales positioning for either of them would emphasize the importance of the service, extreme customer care/service and quality of all the components of the product.

For the funeral services you would emphasize compassion, seeing to all the details thoughtfully, and professionalism.  For the medical equipment you would feature expertise, quality of the machinery, and attention to details.  These are very similar selling points.

In any situation the customer wants to feel their needs will be met by thoughtful service and product expertise ... exciting product or not.