Consumer preferences
Yes. Suppose the consumer has the following utility function:

$$u(x) = - \sum_{i=1}^n x_i$$

Here's a different example, where commodities are goods instead of bads:

$$v(x,y) = -(x-a)^2 - (y-b)^2$$

When the consumer's budget $m$ is strictly greater than $p_x a + p_y b$, then the consumer will not consume all of their budget.