F = m A

Recognise that equation?

F is the net force. Gravity down, hoist cable up, in this case.

Note that this equation does not contain V, only its rate of change. If A = 0 that implies V is a constant. I said nothing of whether that constant is zero or not.

More information, better answers.

That equation does seem a little familiar . I can see that it works on paper but was wondering if it held up in application. I know that it wouldn't defy basic physics/statics, but am questioning if the electric motor or controller would hold up? If you take the motor part out of it it is just a simple counterweight system. However, I am not sure if that is what the motor is made to do and don't know if the controller would throttle the current or if the system would actually hold with no problem. Just kind of a theoretical question with the real-world effects taken into consideration.

What kind of gearing? Self locking worm gearing wouldn't need any help from the motor (so no current draw). Assuming there is no mechanical brake then the motor would have to pull current to produce the torque to hold the load. Most motors don't like high current and slow (or no) speed.

I don't have a specific motor in mind, it was just something I was thinking about in my spare time. It probably wouldn't be a self-locking one or have a mechanical break. If you removed 5 kg from the object you were trying to lift, the motor would be able to pull the object up.

It is good to know that the motor wouldn't like moving something slowly or just holding it in place. That is what I was thinking but it is good to have clarified.

Okay, so I'm getting the question that you wanted to ask might not be the question that you actually wrote out in words.

I'm surmising that the question you wanted to ask is something akin to "How does a hoist hold a load stopped without burning up the motor" or perhaps "What's the minimum speed at which a hoist can raise a load" or something of that sort.

A normal everyday cheap simple hoist doesn't rely on the motor to hold it stopped. The motor probably has a mechanical, spring-applied, holding brake built into it that engages whenever the power to the motor is off (or below some threshold very low voltage). Or, maybe, it has a gearbox with sufficient friction characteristics inherent in its design that it's self-locking. (Worm gears.)

If you are using the motor output torque to balance the load, or moving the load at a very low speed (up or down), then you can't use the holding brake or gearbox self-locking. And in that case ... The motor needs to be supplied current to magnetise its innards in order to develop torque, even if it isn't developing revs. It will, effectively, be stalled. If it is an AC induction motor, then it will have to be supplied a small AC frequency that is just enough to offset the induction motor's inherent "slip" characteristics. In a normal AC induction motor with an integral cooling fan driven by the motor shaft itself, that fan won't be spinning if the motor shaft isn't spinning (and if the motor is spinning very slowly, same goes for the cooling fan). Do that with enough torque output (= magnetising current supply) and the various resistances inside the motor will be making heat. Do that for long enough ... the magic smoke comes out, and then it don't work no more!

There are all sorts of ways to configure hoists.
Always provide ample excess hoisting torque to handle the code required test weight (125% design load). You really really do not want to loose control of the load.

Some hoist are provided with various kinds of mechanical load brakes so the motor never has to get rid of the excess energy of lowering a load. Some of these include worm gears.
Some hoists are provided with dynamic or regenerative load brakes.
All are provided with some sort of holding brake.

If you need a hoist, either use an off the shelf model or engage an expert, designing from scratch is not a simple job.

To answer your question, yes they can. Not all do, but some can hold a load stopped which would drop if the motor wasn't doing the holding.

Generally speaking, once stopped you want the brakes to be applied and the motor shut off. Then, you generate the torque again and release the brakes when you again want to lift or lower the load.