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Assumption: An object has no properties.
I can think of that object as an object with the property that it has no properties, but this is a contradiction to my assumption. Hence all thinkable objects must have at least one property.
On the other hand I can think of an object that has no properties, but then this object will have a property: "The property of not having any properties".
Are we limited to observe and think of objects that have properties?
Your question is an interesting one, and it actually gets at some really fundamental and difficult stuff. In modern philosophical parlance featureless objects are known as 'bare particulars' and there is a literature on them. See http://tedsider.org/papers/bare_particulars.pdf for a recent article. E. Allaire also has an older paper that I think gets anthologized a lot.
Bare particulars are discussed in connection with substance theories. Substances theorists say that reality comes in chunks. Certain things, like atom, or people, or the sun are fundamental, whereas other things, like the atom's location, or the person's smile, or the sun's color are derivative. Call the fundamental things substances.
Now, the question is what exactly is a substance? You might say: "It's the thing that's got the features, the color, the smile, whathaveyou." And that sounds right as far as it goes. But then you ask, well what are the intrinsic features of the substance itself? And it turns out to be very hard to answer that question because every time you try to name some feature that belongs to the substance, it turns out to be one of these derivative properties, like color or whatever. It looks, in other words, like the substance turns out to be just a featureless container for the other properties. John Locke, therefore, famously calls the substance a "something I know not what". That is a `bare particular,' a featureless substratum that holds other properties like a pincushion holds pins.
(Bare particular theories of substance aren't the only theories of substance out there, but there isn't space here for a full discussion.)
The problem for bare particular views of substance is that it turns out to be really hard to explain how there could be more than one substance. Think of Leibniz's Law: Two things are identical if and only if they share all the same properties. But each bare particular has exactly the same properties as every other bare particular, (namely, no properties whatsoever).
That's enough background to get you started.
Of course every object has a property, that of being an object. In the absence of the OP stating what is meant by an object or a property, no other answer is possible.
But it's clear that when it comes to abstract objects, at least, it's not necessarily the case that every object has a property that uniquely characterizes the object. The real numbers form an uncountable set; but if by property you mean a finite-length string over a finite or countably infinite alphabet, there can be only countably many properties.
Therefore almost all real numbers have no property that applies to that number and no other.
What is a thing outside of its qualities, beyond all the forces it exerts on other things, or which are imposed upon it (the affects it generates or undergoes)?
I would suggest looking into Deleuze and Laruelle for more around the question of qualities of objects 'foreclosed' to certain images of thought; and Heidegger/Harman on the question of withdrawn essences of objects.
That said, and (much) too quickly: the idea of a de-qualified or property-less entity appears to raise the tricky question of objects whose essences are in flight, or foreclosed to/withdrawn from the field of thinking.
Such a transcendental reduction of empirical properties is common with the generic objects of science or mathematics -- although there is still in this case a minimal kernel of recognitional content (even if the content is now reduced to an abstract manifold or 'pure' container.)
Are pure metaphysical 'entities' -- i.e., radical immanence, the One, etc. -- somehow beyond being, as in the classical formulation of antiquity? In this case I might suggest it is more like these de-qualified entities expel being(s) beyond themselves.
For instance: if immanence has no qualities (at least that can be validated by philosophical thinking,) this also means it is radically indifferent to the properties that may be assigned to it. This implies a kind of deep equivalence of all theoretical positions: since immanence is not a natural object of thought, but rather profoundly cut out from the philosophical image of thought, it is no longer graspable through a stable perspective or static point of view which would impose sense or an image upon it.
As soon as its an object then it immediately has the property of being an object. I suppose an object could be said not to have properties until percieved but for us to talk about it, it has to. We don't percieve objects directly, only theirproperties. The wavelengths of light they absorb, etc.
Yes, nuclear properties, even with objects that don't exist, as well as ones that exist but just outside of spacetime. Basically the unique criteria that constitute the identity-conditions of a referent. https://www.jstor.org/stable/2214689
