I think that the OP should try to get a better view on what physics, and physical laws, are about. Also ZapperZ is very right when he talks about the need to place things in a context. That's very important. The "context" is the paradigm, or the theoretical frame in which one places oneself to consider the physics of a certain situation, and that context defines the concepts one is going to use, the definition of the words one is going to use, the fundamental principles one is going to adhere to etc...
That's why physicists usually talk about "in classical mechanics, blah blah blah...", or "in general relativity, so so ...". With each context, paradigm, theoretical frame, etc... correspond a number of situations, experimental conditions etc... in which people think the use of that context is appropriate. There are boundary cases where discussion can arise about the applicability or not of this or that context.
Let us take an example: Newtonian mechanics. In Newtonian mechanics, there are things like massive bodies, forces, there is 3-dim space, there is 1-dim time, etc... All this sets up the conceptual and theoretical frame of the paradigm, and there are unwritten rules which make these correspond to observations. In Newtonian mechanics, that correspondence is almost trivial (this is much less so in more advanced theories).
From those basic concepts, one can derive quantities, and one such quantity is "energy". In Newtonian mechanics, there is something like kinetic energy, and under certain restrictions (conservative forces), there's also something called potential energy, and both together turn out to give a number that doesn't change under the advancement of time. That property is called "conservation of energy" in Newtonian dynamics. There's also something like "conservation of mass", but that is an a priori assumed postulate in Newtonian dynamics.
In special relativity, there's also an energy concept, but it is different. Energy is the 4th component of the 4-momentum vector. It turns out that numerically, there is a relationship between the "energy" in the Newtonian paradigm, and "energy" in the special relativity framework. In special relativity, it turns out that the total 4-momentum vector is a conserved quantity (again, it means that this mathematical structure turns out to be the same and unchanging when time advances. Now, there is a quantity one can calculate from a 4-momentum vector, called "invariant mass". Of course the total invariant mass of a system remains invariant given that the 4-momentum vector itself remains invariant. This invariant mass finds numerical agreement with the "mass" which was postulated in Newtonian dynamics.
But this total vector is the sum of contributions, and each of these contributions can have different invariant masses, and these can change during time in special relativity, while they can't in Newtonian dynamics (by postulate). Indeed, it is not true that the "sum of the invariant masses is the invariant mass of the sum". So there is no "conservation of individual invariant masses". Hence you could have 2 massive incoming particles, and have 2 massless outgoing particles. As long as the sum of their 4-vectors remains invariant, that's OK in special relativity. So there is no "law of conservation of invariant mass of components" in SR.
So in order to even consider something like a "law of conservation of space", one should specify in what context, and what exactly one means by that. Is it a number, a mathematical structure ?
In a trivial way, you could say that there is the law of conservation of Euclidean 3-dim space: there is a 3-dim space at a certain moment, and that space remains there after some amount of time (it doesn't become a non-euclidean space, or it doesn't become 2-dimensional or so). Yes.