x1 = x0[::2] is unaliased subsampling, then $E(x_1) = E(x_0)/2$, which can be proven via Parseval's theorem.
For same $x_0, x_1$, however,
E(x1[:a]) = E(x0[:2*a])/2 doesn't hold: that is, unpadding identical portions of the two waveforms that are identical in information contents:
Unpadding aliases (proof omitted) - but even so, above is strange: full signal's energies are equal (within 1/2), but not half.
Is there a relationship, similar to subsampling, but for unpadding, when $x_1$ is an unaliased subsampling of $x_0$? If not, can this be proven? -- Code -- $E(x) = \sum |x|^2$
Note: answer accepted with disagreement on last paragraph, stated in a comment.