Additional related question: Crassus' business model as a fire brigade was to buy houses at a very low price as they burned down in front of their desperate owners, to rebuild and resell for a profit. How would this transaction go down, exactly? Would they have carried carts full of coins ready for the exchange? Or would there be something more similar to modern credit or a bank transfer?
I can't speak to the distribution of assets, but the Romans had an advanced and complex banking system. Roman bankers could handled most of the functions modern banks can handle, including holding deposits, lending for interest, balance transfers, and the kind of purchases you're describing. The Romans also had a system of civil courts which, among other things, could enforce contracts.
So if Crassus could show up, barter with the desperate owner, and agree on a price, it would be perfectly possible to get the owner to sign a deed, and then to give him in return a draft on his bank (functionally, more or less a check) and have a legally binding transaction. And if, once the fire was out, the owner thought he could go back on the deal, Crassus could certainly have taken him to court and sued him to enforce the contract. There was certainly no need to be traveling around with wagonloads of money.
Sources:
On banks, Jean Andreau, Banking and Business in the Roman World. Cambridge and New York: Cambridge University Press, 1999
On Roman courts and procedure, a very in-depth treatment from a legal perspective is.
Metzger, Ernest. “Roman Judges, Case Law, and Principles of Procedure.” Law and History Review, vol. 22, no. 2, 2004, pp. 243–275. JSTOR, www.jstor.org/stable/4141647.