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I know tens of big websites which has partnered with them now there is the same content on all websites.
I am wondering,is it possible that search engines can penalize my website if i partner with that company too and place the same content?
There is a link back to original provider on every page.
Your subdomain probably won't rank because it is dup content.
I would try to find out if the site offering the program is spamming or penalized in some way, because if they are, and you link TO THEM from your subdomain, it could darken the reputation of your subdomain, which is worse than your subdomain simply not ranking. If that happened, and you linked to your subdomain from your main site, that might even hurt your main site to some extent (not sure about that, and many other factors involved).
What I cannot see is any upside - what will you gain by setting up a domain which perfectly duplicates thousands of others, and will never be listed in search engine results.
What will the web gain by having a few thousand more clone sites?
Why would you go to all this trouble simply to provide a promotional link to the 'main site'?
They gain. You don't.