“BIG” is typically a reference to the “Built in Gains” tax that applies to S-corp’s…but it’s a concept that’s thrown about in the partnership arena as well, so I’m fine with you using it.
What you have is a 704c issue, but that’s for the partnership to figure out, although you’d want to negotiate whatever method is most favorable to your client. There wouldn’t be any personal gain on client’s contribution.
The issue is whether or not the partnership holds the property for the requisite purpose (i.e. business, investment, rental) prior to the exchange. If it doesn’t, that could be an issue. But this would be a partnership issue, largely outside of your client’s control. The only way your client could control it, if client thinks this is a bogus 1031 transaction, is to not contribute the property in the first place.
If your client makes the contribution, and if your client gets a K1 with no gain on it, such that the partnership took the position that the exchange qualifies under Sec 1031, then you’d have to go with that treatment. (Sounds doubtful that the partnership would do anything different, based on what you wrote). If it later turns out that the IRS disputes 1031 treatment, then client would be stuck with whatever the final outcome turns out to be.