Hello, I will try to answer this as best I can, I wrote my Masters's Thesis on Canada's involvement in Yugoslavia during the 1990s. So although I didn't specifically focus on communism I think I might be able to tackle this.
To admins, I can confirm the above if need be.
Okay, caveats aside. At the outset of the Yugoslav collapse, there were a number of factors leading to disintegration. Politically the luster of the communist party had been waning, the struggling economy being a large factor for that. The collapse of communism in Eastern Europe and the spread of nationalism added to this. Keeping in mind that there has been a push for more state autonomy during this time as well.
Western intelligence agencies had already been discussing the likeliness of a Yugoslav collapse along ethnic lines and predicted that it could / would be violent. Also, some of the financial support for these movements came from the ethnic diasporas abroad.
So generally speaking what you had was the confluence of the following factors:

Internal ethnic divisions, which existed under the surface of an otherwise seemingly united country, were somewhat held together for the most part by Tito's personality.

But also (and I think more importantly) the fact that early in the cold war Yugoslavia had broken politically with the USSR which made it a good destination for US and Western investment for a couple of decades. As the impression that investing in Yugoslavia as a good policy disappeared in Western policy-making so did the strength of its "functioning communist economy".

The push for greater nationalism within the constituent states was given support from the diaspora communities.

And (this is my view) a generation of poor self-serving political leaders.

So when Slovenia declared independence and took over border crossings it was still the Socialist Federal Republic of Yugoslavia that responded. At the time Ante Markovic was the president of SFR Yugoslavia and under his direction, the JNA was sent into Slovenia. So at this time, it was a communist government in Belgrade calling the shots. This government was still multi-ethnic (Markovic being an ethnic Croatian) and the belief was that Communist Yugoslavia could be preserved. Now that being said, there wasn't a full assault sent against Slovenia as the government in Belgrade was more concerned with the situation developing in Croatia. Regardless, hostilities in Slovenia were short and ended with the JNA withdrawing from Slovenia.

With that (although not just that) Slobodan Milosevic looked to cement his power in Serbia. He still considered himself a communist / socialist and nominally and publicly held to this although he was certainly stoking nationalist feelings as well. So his push was to gain power from Markovic and other Communist Yugoslavia leaders in Belgrade. In Croatia, Franjo Tudjman was gaining power and eventually declaring independence and so a desire to hold power in Yugoslavia wouldn't be of any interest to him or his party because they were looking for Croatian independence. This eventually led to the war in Croatia which was initially between Serbs in Croatia v the Croatian state and then involved the JNA sent from Belgrade.

So, although there were citizens and politicians who were pro-socialist, pro-communist, and pro-Yugoslav, actors within and out of the country created a situation where their socialist ideas were drowned out.

It's not too dissimilar to what is happening in Afghanistan (from the perspective of an analyst looking in from the outside). The expectation in Afghanistan was that the Taliban would take over the country and put pressure on the cities held by the Afghan government but the fact that it happened so fast was what was a shock. Similarly in Yugoslavia, the death of communism and a communist government was expected and as nationalism was on the rise this became more likely but the expectation that the point of no return would come so fast caught many off guard. So once the bread was sliced you couldn't put the loaf back together. So there wasn't any explicitly communist soviet red flag waving milita, para-military, or army. But in the outset the JNA and the last bits of the communist government would have been what remained of communism in Yugoslavia.

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I can elaborate on specific parts of this as I didn't go into as much detail as there possibly is for each factor. But hopefully this helps a bit.

References:

Peacekeeper: The Road to Sarajeveo. Gen. Lewis Mackenzie

The Serbs. Tim Judah

The Balkans. Misha Glenny

Ghosts of Medak Pocket. Carol Off

To kill a Nation. Michael Parenti

From Peacekeeping to Peacemaking Nicholas Gammer

Among others...