It's a potato potahto kind of thing @Michael Bishop and @Eric Mayer. We're all singing on the same choir page. It's just that syndication as a term has been hijacked in this market for a single product.
It its pure form syndication is really just a bunch of folks pitching in to purchase and manage an asset (whether race horse, oil well, or apt complex).
The type of syndication that's talked about the most here is the LP syndication usually with a 506 b or c SEC filing. I'm a simple guy so all of that is kind of "blah blah blah" a foreign language to me. What is important where I live is that these types of syndication almost always cannot accept 1031 money.
The reason is that purchasing into a syndication of this sort you are purchasing a membership interest in the entity and not the real estate itself as required by 1031. The only way to make one of these work for 1031 is if the 1031 investor can become a tenant in common with the LP in ownership of the asset. To do this the syndicator has to be willing to jump through the hoops. And more importantly the lender to the LP has to be willing to split the ownership of the asset. I've seen a few instances where this can happen - especially if the LP is funded internally and the investor is a tuna. But they are rare as @Michael Bishop said.
If we broaden the term syndication to mean what it really means - a bunch of people putting money together to buy and manage and asset then two more types of syndications are available.
Tenants in Common (TIC) - Just like it sounds. Everyone owns a % tic interest in the actual property. Safe Harbor from the IRS in rev proc 2002-22. Not very common because theres governance hurdles and debt financing hurdles to over come. But they are indeed out there. And they are 1031 compliant. More common 2-3 years ago. Now being overtaken by the other "syndication that is 1031 compliant.
Delaware Statutory Trust (DST) - You own a membership interest in the trust which sounds like it won't fly for 1031. But wall street saw the incredible success of TICs in 02-04 and wanted in on the action. So the SEC and the IRS and a few dozen Philadelphia lawyers (general term not actual PA attorneys) got together in a back room somewhere and Boom! - Out comes Rev proc 2004-86 . A safe harbor for 1031 exchanges going into DSTs. Very easy for a 1031 investor to get into DSTs. And this is more the question that @Eric Mayer was asking.
But here's where it gets interesting Eric. The reason DSTs are popular with 1031 investors is that they are 1031 compliant. But they are not popular with the contemporary syndicator for a couple of reasons. The structure is different so they're maybe not as familiar with the DST as with an LP. A DST is hard to structure to accommodate syndicator waterfalls and uneven payouts at sale. And There has traditionally been a pretty big difference in the cost to set one up.
So as it falls out - Users prefer one model. "syndicators" prefer another model. one is very easy to work with 1031. One is incredibly difficult. Both have their uses. We're putting way more people into DSTs followed by only a small amount of TICs and very few syndications since the investor has to be willing to pay the tax and then use the net after tax to invest in an LP syndication.