The Name of the Rose by Umberto Eco claims that Pope John and his allies endorsed art depicting Jesus with purses and coins to challenge the Franciscan assertions of apostolic poverty, even giving the crucified Christ a money pouch. Does this have a basis in reality?

The Name of the Rose is my favorite book of all time, and tragically, I will insert myself into any /r/AskHistorians thread in which I find it.

For anyone who's unfamiliar with the novel, or who's read it but has forgotten the context, what /u/eeeeeep is referencing is a discussion between several Franciscans a little more than halfway through the story, which takes place in the fall of 1327. The date is important for a reason we'll get to in a moment:

(Ubertino said ...) "In every other situation he (Pope John XXII) has displayed a diabolical skill in collecting money. He is a Midas: everything he touches becomes gold and flows into the coffers of Avignon. Whenever I entered his apartments I found bankers, moneychangers, and tables laden with gold, clerics counting florins and piling them neatly one on top of another .... And you will see the palace he has had built for himself, with riches that were once attributed only to the Emperor of Byzantium or the Great Khan of the Tartars. And now you understand why he issued all those bulls against the ideal of poverty. But do you know that he has driven the Dominicans, in their hatred of our order, to carve statues of Christ with a royal crown, a tunic of purple and gold, and sumptuous sandals? In Avignon they display crucifixes where Christ is nailed by a single hand while the other touches a purse hanging from his belt, to indicate that he authorizes the use of money for religious ends...."

"Oh, how shameless!" Michael cried. "But this is outright blasphemy!"

As with everything else in the novel, while the discussion is outwardly about one thing, it's actually about a lot of things. The fight between Pope John XXII and the Minorites is a running theme in The Name of the Rose, and Eco chose its setting very carefully. This conversation among several Franciscan characters is set against the backdrop of John's demand that Michael of Cesena (the minister general of the Franciscans in both real life and the book) come to him in Avignon to make the Franciscans' case. His colleagues are trying to convince him that he isn't going to get a fair hearing and nothing good will come of it.

They were correct. Both the historical and the literary Michael are summoned to Avignon in early 1328, decide to go, and are shortly afterwards imprisoned by John for their refusal to cave on the issue of poverty.

So why does John XXII care so much if some monks want to be poor? Wasn't Christ poor anyway? It's not about poverty. Well, it sort of is, and it sort of isn't. "Poverty" here is a cipher for an enormous political and economic mess concerning:

The right of the mendicant orders to remain "poor," and the logistical headaches this entails: John wrote a 1322 bull Ad conditorem canonum pointing out that the mental gymnastics required for the Franciscans to pile up political influence and buildings and land and goods but not "own" any of them were kinda dumb. If you're "poor," but have 24/7 access to a staffed mansion and a private jet stocked with Chateau Lafite Rothschild and truffles at your complete disposal, are you still "poor" no matter how much you insist that you have the use but not the ownership?
What the Minorites see as the corruption of the Church and its mission: Unfortunately, that puts the Minorites in agreement with several Christian sects that were previously declared heretical. As William of Baskerville observes in the novel, this is a very dangerous tightrope for the Franciscans to walk; they want to be loyal enough to the Church to keep themselves from being declared heretics, while pushing for reforms that heretical movements had wanted. Further complicating the issue is that having the Minorites around can be politically useful for the Church at times, hence the battle to gain more control over them.
The incredible wealth that the papacy either possesses outright or to which it has access. This wasn't a new issue in 1328, and it remains an issue now. One of the biggest symbolic acts by a Pope in the 20th century was Paul VI's renunciation of the papal tiara and the establishment of the inauguration, rather than coronation/crowning, of new popes. (Also, pop quiz: Why did the current pope pick the name Francis?) Many Catholic theologians have argued that the New Testament's account of Jesus and his especial concern for the sick, the poor, and the dispossessed coexists uneasily at best with an enormously wealthy church.
And perhaps most importantly of all, the balance of power between secular kings and their religious counterparts. Who is the ultimate authority? Should kings be crowned by bishops? Do popes have the right to approve or depose secular rulers? Is the Church subject to laws written by secular authorities? Who's actually in charge around here?

There is an awful lot that could be written about all of this, but I would encourage people to both: a). Read the book, and: b). Look into the background of the novel. It's fascinating.

So, getting to your actual question --

An art historian is the best person to answer this and I really hope one shows up. I was curious about this too and have looked into it on and off for years. The Name of the Rose is beautifully researched and an incredibly accurate depiction of both the time period and the political environment, so I was operating under the assumption that Eco had specific pieces in mind when he gave that line to Ubertino. Unfortunately, I have yet to find any surviving piece that shows what Ubertino claims. That doesn't mean it's not out there or never existed -- just that I've never found one. It's a pretty frustrating state of affairs because Ubertino's claim is so specific that you'd think finding an example would be easy. Then again, we'd also consider these pieces fairly controversial today, so there's always the possibility that, if they did exist, when the political circumstances behind the fight over poverty changed, they were quietly removed from display and either destroyed or consigned to the dusty corner of an archive somewhere. Another and depressingly likely possibility is that I've passed over examples without realizing that I did, and I'm hoping that /r/AskHistorians can turn up someone with a better background in art history.

You can find depictions of Christ associated with richer clothing and symbols of temporal power, but this seems to be most associated with the Salvator Mundi tradition. Problem is, I don't think this was common in Western art until a century or more past the events of The Name of the Rose, and it seems like an awkward fit at best for what Ubertino was discussing. Again, we need a pocket art historian for this.

If there aren't examples out there, Eco may have taken some liberties for the sake of the novel. In fairness to him, it may even have been in service to characterization, because both the historical Ubertino of Casale and his counterpart in the book were firebrands. The real Ubertino was a huge pain in the ass to multiple popes, and his most famous work, Arbor Vitae Crucifixae Jesu Christi, names two of them as harbingers of the apocalypse. (It didn't go over well.) William in the novel considers him a brilliant but often dangerous extremist who inflicts needless damage on his own cause. Getting carried away and exaggerating the details of what he'd seen in Avignon wouldn't be inconsistent with Eco's characterization of him.

Batting clean-up: St. Matthew is sometimes depicted with a money purse to reflect his former status as a publican/tax-collector. Judas is much more frequently depicted with one, both to reflect his greed -- he's the apostle who sells Jesus out for thirty pieces of silver -- and because John 12:6 records him as the group's treasurer who supposedly dipped into the purse for his own ends.