Consumer preferences I want to know under what preferences relation will I not want to consume all of my budget. Because if my preferences are strictly monotonic, strictly convex or convex, even LNS or continuous. I would consume all of my budget. Are they any situations where I would not?     

Edit: when I meant preferences I am treating each individual case i.e. if it is LNS it is not convex (necessarily)
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.