My syndicate manager let's everyone know his login details so we can always check what is happening and check up on our winnings, and for general transparency that all our money did go on the tickets and he isn't pocketing some of it.

Now if he were running off he could easily change it to run off, or withdraw and just not pay. But frankly I trust him a great deal (our work requires it). Further he said there are actual ways that you can enforce it anyway without written contracts, as a verbal agreement is also binding (in English Law I think) and when 20 of you stand up and say syndicate manager said these were the terms then that would be enforced.

Still doesn't stop the fleeing the country option you mention, I don't think anything would... If you don't think you can trust them to do that, maybe you shouldn't join, just don't get salty if they win.