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On the one hand covariance matrix can't contain negative values by definition, but as far as state covariance matrix innovated by subtraction:

$$\mathbf{P} = \bar{\mathbf P} - \mathbf K\mathbf P_{z}\mathbf K^\mathsf T$$

it's possible to get negative value.

Can state covariance matrix in Unscented Kalman filter contain negative values?

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actually a covariance matrix can have negative values off the diagonal. variables can be negatively correlated, but the diagonal terms are variances which must be positive.

The update you show can be a problem which is why updates of $P^{-1}$ are preferred.

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