I am a patent attorney generally on the patent owner's side.

Signing such a clause should make you nervous. You don't want to be responsible for the major company's infringement. The major company is likely getting more benefit out of using your software than your company is making by selling licenses.

The previous gentleman's answer is incorrect. Anyone can be sued for patent infringement if they make, sell, or *use* the claimed invention. It depends on the claims in the asserted patent. Based on experience, it's much more likely that the larger entity would be sued for infringement.

A patent infringement case could cost anywhere between $350k-$5M+ USD.
http://www.cnet.com/news/how-much-is-that-patent-lawsuit-going-to-cost-you/

In order to properly answer your question, I would need to know why you feel it's "very unlikely" that someone would sue the major company for using your software.

If the major company won't back down on this provision, the best thing you can do is determine if you need IP (defense) insurance. If a patent attorney determines that it is necessary, raise the price of your license and get IP insurance.