However, there is no total and complete lack of government. In fact, local councils (comparable to Municipalities or County level in Canada and the USA) continue to operate.
Here is a map of the councils and their political makeup.
As you can see, the map is colour coded.
Here is another map showing the party that finished in first in each DEA
The DEAs are generally similar in size, but not exactly. Armagh (district 6 on the upper map) would need an extra DEA for their DEAs to be similar in size to the others, while Belfast, the Capital, would need three more. Regardless, you could consider this a fun experiment in "what if Northern Ireland had FPTP elections" in which case you would see the following:
Meaning the DUP won exactly half the DEAs in Northern Ireland.
Despite this, none of the 11 councils are controlled by a single party.
Control of local councils, Unionist vs Nationalist, can be seen in the upper right. Belfast is balanced, and as such, neither 'side' has control. For reference, the Westminster result is shown in the upper left.
The "long story short" of all of this is that local government does, in fact, continue in Northern Ireland, even if Stormont is shut down. Westminster itself also continues. In the Canadian context, it is like both Toronto City Hall and the Federal government operating while the Provincial level is not.
Prior to 1972, Stormont, and local government, was dominated by Protestants, mostly due to the design of the system.
From then to 1998, despite repeated attempts at a working assembly, local councils remained the only stable local governance.
In short; Northern Ireland has been through all of this before.