How does negative selection in the thymus get around viral antigens that invade the thymus?

Precursor T-cells undergo positive and negative selection in the thymus. Negative selection eliminates T-cells that bind strongly to self antigens (e.g. produced by the AIRE gene).

However, how is it ensured that only SELF antigens are tested for during negative selection? Perhaps some virus antigen has invaded the thymus and all T-cells that strongly bind with it are also eliminated. This would result in no T-cells being released against that virus, and hence no immunity against it!

How easy is it for a virus to invade the thymus, and how can the purity of self antigens be maintained if it happens - so as to ensure that only self and nothing but self antigens are presented to T-cells during negative selection?