Fieri potest with final ut or explicative quod

Question

Suppose I want to say:

It can happen that my horse dies.

I do not want to say "my horse can die", but I want to keep this structure where the thing that happens is in a subordinate clause. This helps clarify the structure in some longer sentences and it also gives a different tone.

"It can happen" is "Fieri potest", but I can think of two options for the rest:

Fieri potest, ut equus meus moriatur.
Fieri potest, quod equus meus moritur.

Are both of these valid? If both are grammatical, is there a difference in tone? Are there even more ways to form a similar subordinate clause?

I see the following difference between ut and quod (which I hope is clear enough from the more emphatic versions), but I am not sure if the Romans would agree:

It can happen so that my horse dies.
(Ita) fieri potest, ut equus meus moriatur.

The thing can happen that my horse dies.
(Id) fieri potest, quod equus meus moritur.

Answer 1

I've never seen fieri potest, quod.

I find however several examples of fieri potest, ut subjunctive in the corpora; the first two are:

Si hoc fieri potest ut in hac civitate quae longe iure libertatis ceteris civitatibus antecellit quisquam nullis comitiis imperium aut potestatem adsequi possit, quid attinet tertio capite legem curiatam ferre iubere, cum quarto permittas ut sine lege curiata idem iuris habeant quod haberent, si optima lege a populo essent creati?
—Cicero, De Lege Agraria, 2.26.1

Neque enim fieri potest ut aliud iudicari de iure, aliud responderi oporteat, nec ut quisquam iuris numeretur peritus qui id statuat esse ius quod non oporteat iudicari.
—Cicero, Pro Cæcina, 65.1

I myself don't mistake it for a purpose clause, especially since si fieri potest shows up a lot and seems to be a locution for "if possible," so I take it as a clue that what's coming up next isn't purpose. I'd mistake quod, though, for "because," and it would cause all kinds of confusion. (Not that that's unusual for me.)