This is not a short answer I hope they allow all of this to be placed. I would like to know a bit more information. First I see the creative and production side of this venture but what about the other critical component. SALES. It appears the factory wants to make better Margin by having their own collection and not just manufacture for other brands. A good thing in theory but you need to consider the actual team before you invest what could be incredible work on an start-up unprepared to get those goods to market.
You should find out exactly what the long-term goals of the group are and exactly what if any distribution (sales) plans are in place before submitting any kind of offer sheet. You are a designer
so make sure the team around you is complete (committed sales entity) in this case.
Factory financed deals are a dime a dozen but often lead to a lot of great product not making it to the sales floor because the lack of sales and marketing expertise. Been there, done that.
The factory ends up with great samples to show its existing client base which you designed for free if you do not get a salary.
Once you make sure there is a committed structure to getting the PRODUCT to market properly then do the following.
Form a new company. They are already in business and you do not want to have anything legally to do with THAT business. If you are not then you should form an LLC for yourself.
Your LLC and their Legal entity form a new company. ACME T-shirt company for the lack of a better example, to design, manufacture, distribute, ship and collect on your creations.
Here is where money and ownership come into play.
IF YOU WANT A SALARY OR RETAINER then you need to define how you want the money. I generally suggest an up front zero or low-interest LOAN against future profits that will allow you to function as an individual and company. Borrow enough to stay comfortable while you put your heart and soul into getting the collection off the ground. Trust me they will not loan you a penny more than they want to but they will understand you need to survive in order to get the work done. So be reasonable. Offer to accept the loan in monthly installments (6 to 12 months) so that each entity can make sure mile post are being hit in the development of the company, brand and product. This is easier on the pocket and assures that changes can be made if necessary.
Lastly. The split should remain 50/50 of the net profits for the ACME entity. Remember the factory is going to pay itself for making your goods. Generally under its normal profit earning structure. After that they get another 50% of the profits after the cost of selling. If your brand is successful you will have more than enough money to repay the loan and do well for your OWN company.
Hope that helps
forgive any typos, just blazed through the answer.