For linear regression to be a suitable model the data need to meet certain criteria:

1. The mean response is a linear function of the predictors.
2. Model residuals are conditionally independent.
3. Model residuals are distributed with conditional mean zero.
4. Model residuals have constant conditional variance.
5. Model residuals are conditionally normal in distribution.

The response you describe fails to meet (at least) criterion 5, so the General Linear Model does not apply to this example.

For the General Linear Model to be suitable the data need to meet certain criteria:

1. The mean response is a linear function of the predictors.
2. Model residuals are conditionally independent.
3. Model residuals are distributed with conditional mean zero.
4. Model residuals have constant conditional variance.
5. Model residuals are conditionally normal in distribution.

The response you describe fails to meet (at least) criterion 5, so the General Linear Model does not apply to this example.

As discussed in the comments, this does not prevent the calculation of RSS, which you have already noted is 0/0, an indeterminate form.