ArcMap (and ArcGIS Pro's map and scene) can change a data layer's coordinates in-memory or "on-the-fly."
A data layer that has no coordinate reference system / spatial reference cannot be projected on-the-fly. The layer's coordinates will just be displayed as they exist. No assumption is made on what the coordinate reference system might be.
If a data layer with no coordinate system is added to ArcMap as the first layer, the data frame itself will have no coordinate system and you will find that the map scale control is grayed out, and some features of the measure tool don't work, etc.
As several people commented, if the data layer with no coordinate reference system does line up with other data layers, it probably has the same coordinate reference system as the data frame's. Where this can get tricky is that the data could be in a similar geographic coordinate reference system (datum) but not exactly the same as the data frame's. For instance NAD 1983 (2011) versus any of the earlier. If you're not comparing against very accurate imagery (sub-meter) or very specific features that are common to both layers, you won't be able to determine beyond a doubt the exact geographic coordinate reference system.
If you're reasonably certain that the coordinate reference system of the 'unknown' data layer is the same as the data frame's, use the Define Projection tool or the data layer's property page in ArcCatalog to set the coordinate reference system.
Note: coordinate reference system is an ISO term; Esri uses coordinate system. ISO's coordinate system has a different meaning than how Esri is using it.
Disclosure: I work for Esri.