Neither MPS nor MPC can ever be negative. MPS is the ratio of additional saving $\left(\Delta \text{S}\right)$ to additional income $\left(\Delta \text{Y}\right)$. Likewise, MPC is the ratio of additional consumption $\left(\Delta \text{C}\right)$ to additional income $\left(\Delta \text{Y}\right)$. The ratio $\left(\frac{\Delta \text{S}}{\mathrm{/\Delta }\text{Y}}\right)$ refers to slope of the S-function which is always positive (because of positive relationship between S and Y). Likewise, the ratio $\left(\frac{\Delta \text{C/}}{\Delta \text{Y}}\right)$ refers to slope of the C-function which is always positive (because of the positive relationship between C and Y).

APC can not be negative because even if there is 0 level of income, there has to be some consumption (autonomous consumption). On the other hand, APS can be negative which is nothing but dissaving. APS can be negative in a situation where S is negative (or when C > Y). This implies that the consumption is greater than the income.

Example: $\text{Y=60, C = 50, S = -10}$