This question could have several different answers depending on when you might want them to stop.

A background:

The Mongol Empire under Genghis was the unification of various nomadic tribes across the Eurasian steppe - being tribes, they were more accustomed to raiding and looting towns rather than conquering and consolidating their empire. Looking at this image of the general area you can see that the Mongols would be able to quite easily find wealthier societies near them that were worth the effort.

As we know, nomads of the Eurasian steppe were mainly pastoralists, herding their livestock to new grazing regions whilst also bringing their entire living area. Being pastoralists, they could not generate the goods that wealthier societies could produce (China: silk, tea, china/porcelain, as well as many other products that civilisations across Asia produced) and so in turn had nothing to trade for these goods.

Because of them:

• being unable to create a fully self-sustainable source of income

• being unable to enjoy luxurious goods

whilst being being bordered by significantly wealthier societies across Asia that were also close to the steppe, the Mongols were pretty much in the best position to come into all of them.

However, invading other areas however could then result in two things - either the society you're invading has allies that will fight you too, or not - which as a result stimulated further conquests. This doesn't apply to everything, as most obviously seen in how the Mongols managed to conquer China - China was fragmented into three different dynasties, the Song, Jin, and Xia, and so due to the political instability and the unwillingness to help each other, the Mongols managed to establish the Yuan dynasty of China.

Coming back to the point on wanting more goods, the Mongols wanted as well to re-establish the lucrative trade route known as the Silk Road, which was previously under control by several empires throughout Asia. They did this by creating a single, unified empire that spanned the entire distance they could increase profits while making it relatively safer for merchants, and so justified their continual expansion.

Back to the question: Whilst the history of the empire was interweaved with expansions and conquests into other lands, knowing whether or not the Mongolian Empire would have suddenly collapsed is rather hard to predict.

Genghis' own belief in a unified Mongolia, where previously several tribes within Mongolia were consistently fighting with each other whilst having issues with their surrounding empires, was the main driving force in establishing the Mongolian empire. However, this came with the issue that when Genghis died, the empire was split up between his four sons into various Khanates, becoming individual, separate societies instead of a single unified entity.

However, we do know that an era of peace within the empire did exist, Pax Mongolica. The re-establishment of the Silk Road meant that a continuous, uninterrupted flow of trade goods was able to go from East to West - merchants were able to travel for the most part under safe conditions, notably with people such as Marco Polo being able to travel across the entire breadth of Asia.

Similarly, a unified code of law, council and legal system, all suggest that the empire would not have swiftly collapsed upon the sudden stop of expansion. However, this also is a point of issue as we know that after the deaths of Genghis Khan and his successor Ogedei, the Empire largely fell into disunity, so again it would depend on what time period you're referring to when the Empire stopped conquests.

Some nice things to read further into this:

The History of Mongol Conquests - Saunders, J. J.

The Mongols - Morgan, D.