I have been on a fruitless search for a technical partner to help me build a web startup. In the meantime, I went ahead and had the MVP built by an offshore company. They've done a pretty good job, are very responsive, and I'm pretty happy with them.
Since my luck with finding a technical person still hasn't turned around, I would like to enter a partnership agreement with the offshore company.
I cannot offer any more funds but I would like to offer them equity. Also, I will continue my search to find a technical co-founder so I would like to take that into consideration as well when deciding upon the terms.
Since I will be approaching the offshore firm with this idea, I was wondering if I could get the help of the people on this forum with regards to the type of terms I should be thinking about.
You seem to have successfully navigated the treacherous waters of outsourcing. That's a strong point right there.
If I understand your question properly, you are basically running out of money, so you can't pay the offshore company anymore (at least not at the desired level). Since you are happy with the quality of their work, it's ok for you to switch to a more equity-based compensation. I have no idea if that would be ok for them, though. You need to ask. Usually, the whole point of offshore is to work for cash, equity is just too risky.
You may be able to lower the cash rate by offering equity, so keep an open mind. And just ask them. Be ready to be convincing when they ask you how likely it is that your project will one day generate profits. You are asking them to invest their resources into a highly risky venture.
If you are a US (or other first world) company and you are going to have a substantial portion of your equity owned by a foreign entity be aware that this will have substantial tax and reporting implications.