I have 3 toilets in the house. The one in the basement I recently (about 6 months ago) replaced so that they are now all 3 the same (american standard low flow). It was working fine until about 10 days ago. When I flush it the water stays in the bowl and then fairly quickly drains out until there is not enough water to fill the bottom. When it is draining I can hear the water draining. I have added water to the bowl and it too drains quickly down to the point where the bottom of the bowl is not completely covered. I have plunged it multiple times to no avail. Every once in a while it will flush (somewhat) but not as it did when I first put it in. I am the only one who uses this one (just the wife and I) and nothing fell into it. I do use a cleaning tablet (Clorox cleaner) that is in the tank (it dissolves over time) and it is not obstructing the flapper. We have owned the house for 22 years and this is the first time I have had an issue with any of the toilets.
If you have a plugged sewer vent or a plug in a line to the vent, then water can get sucked out of the trap in the toilet. I believe that this is the reason low water in the bowl occasionally occurs in plumbing that has no permanent fault.
I just poured a bucket of water into a properly operating toilet and the water drains down to a very low level in the toilet. So this is normal. The water supply system in the tank is supposed to continue a gentle flow into the bowl after the flush is finished to raise the level in the bowl to the height that the design of the toilet trap allows. In your malfunctioning toilet the water supply may not be directing the flow through the small flexible hose into the overflow tube. With the tank lid off compare a flush in the basement toilet to a flush in one of the properly operating toilets.