In general, deterministically related regressors are not prohibited in a regression model.
In introductory econometrics textbooks one may encounter a model of the form
$$y=\beta_0+\beta_1 x+\beta_2 x^2+\varepsilon$$
This is one special case of what you are concerned about, if I understand correctly.
A restriction in the regression model is that the regressors cannot be linearly dependent. (For example, you cannot have $x_1=\alpha_0+\alpha_1 x_2$.) If they are, the marginal effects of the linearly dependent regressors cannot be disentangled; the $\beta$ coefficient vector taken from the regression $y=X \beta + \varepsilon$ is not unique ($X$ is the design matrix where each column is a different regressor). Other than that, you may have deterministically related regressors.
However, you have to be careful interpreting the estimated coefficients when the regressors are deterministically related. If you have both $x$ and $x^2$ as regressors, you cannot say that "keeping all other regressors constant, a unit change in $x$ brings a $\beta_1$ change in $y$" -- because when $x$ changes, $x^2$ also changes.
depending on the value chosen for a given predictor <...>, the possible values for another predictor are restricted to a subset of values
is more general than what I have analysed above, but I think the same logic applies.