Borrowed chords, or chords making use of mode mixture, are handled similarly to their diatonic versions in terms of voice leading, e.g., $\left.\text{ii}^ø{}^{7}\right.$ is handled similarly to $\left.\text{ii}^{7}\right.$. In any of the borrowed chords with ♭$\hat{6}$ , resolve this tendency tone down by step whenever possible.
Another situation where you may encounter a borrowed chord is the $\left.\text{V}\right.$–♭$\left.\text{VI}\right.$ cadence, which should be handled exactly as the deceptive cadence in minor is handled—resolve the 3rd of the $\left.\text{V}\right.$ chord up by step and move the other two voices in contrary motion to the bass.
There are no specific rules for other borrowed chords such as ♭$\left.\text{III}\right.$, ♭$\left.\text{VII}\right.$, $\left.\text{i}\right.$, and $\left.\text{v}\right.$; simply voice lead them as smoothly as possible while avoiding objectionable parallels.