We charcterize lower semicontinuity of integral functionals with respect to weak convergence BV (the space of maps with bounded variation), including integrands whose negative part has linear growth. In addition, we allow for sequences without a fixed trace at the boundary. In this case, both the integrand and the shape of the domain boundary play a key role. This is made precise in our newly found condition quasi-sublinear growth from below at points of the boundary which compensates for possible concentration effects generated by the sequence. We use our result to find relaxation in BV of coercive integral functionals with linear growth at infinity. This talk is based on joint work with M. Baia (Lisbon), B. Benesova (Würzburg) and S. Krömer (Prague)