We’re in discussions with an investor and they want us to get “Investment Liability Insurance” -- which doesn’t make sense to us or our legal team. Has anyone ever heard of such insurance and what does it cover?

You typically never want to do this, for multiple reasons. Some later stage companies get conned into this, but unless you're at the PE stage and getting underwritten by an investment bank, you're either too early to bother/dealing with an unsophisticated investor. I'm sure if there's other lawyers on this channel, they'll echo the same sentiments.Investments by nature are high risk, and a well written subscription agreement or stock grant will have provisions laying out in detail that the buyer is engaging in a high risk investment and has fully understood the risks associated with and nature of the investment. "Investment Liability Insurance" for a seed stage company is just a fancy workaround to convert an equity investment into debt financing where the principal is guaranteed by a third party. I've only encountered investors making these kinds of requests in two scenarios - either unsophisticated investors who really shouldn't be investing in early stage companies at all, or PE investors who want the same the preferences in an early stage deal. Neither is appropriate for your companies is you're both early stage. Whether or not you accept the terms comes down to a business decision of if the investor is really worth that much to you.