Pressure is the magnitude (absolute value) of the force over the area, so how can that result in a negative value for pressure as would happen in certain circumstances?
The term “negative pressure” is often used in engineering to refer to a situation in which an enclosed volume has lower pressure than its surroundings. If the a region is surrounded by more pressurized area around it would cause substances to flow inwards and thus the term negative pressure.
Pressure is not an absolute value. It might be helpful to know where you got that idea from. I can theoretically completely evacuate a chamber so that one side of a pressure transducer has "zero" pressure and then claim that what I'm measuring (on the other side) is the "absolute pressure". The problem with that is that I can't completely evacuate any chamber, nor can I prove that once I've reduced the measurable gas (or liquid) present to below my detection limits that there isn't some kind of "aether" present.
OTOH, we can approach zero pressure "in the limit" and we can, via other experiments, show that there is no "aether". The Casimir Effect between two plates placed close together is an example of the existence of pressure in the absence of "everything". So, for practical purposes we can claim knowledge of absolute pressure values, even though all measured values are relative.
In the USA, relative gauge readings are often recorded as having units of psig or pounds per square inch gauge pressure, which means the pressure excludes ambient air pressure (which depends on altitude, weather, and temperature (among other things)), other gauges have units of psia (pounds per square inch absolute) which are based on a perfect vacuum being the zero point. It is important when using any pressure gauge to know what the value is relative to (to ambient air pressure, to a standard atmosphere (and which standard atmosphere!), or to a 'full' vacuum).
Another way to put this is that if we assume we can obtain a vacuum, then we can measure relative to it and claim the result is "absolute". While reasonable and quite solidly based on our understanding of the nature of our physical world, we can not prove it is true without making underlying assumptions about how nature influences its measurements.