The Zilber-Pink conjecture for a curve in a semiabelian variety G predicts that, if the curve is not contained in a proper algebraic subgroup of G, then its intersection with the codimension 2 algebraic subgroups is a finite set. In the case where everything is defined over a number field, this has been proven by Barroero, Kühne and Schmidt, building on previous work of Habegger and Pila. More recently, a variation of this problem has emerged, where one looks at the intersections of a curve with the codimension 1 algebraic subgroups, but one only considers those points in which such intersection is singular. In this talk, we will show that this set of intersections is also finite in the case of curves in families of abelian varieties and curves in split semiabelian varieties, generalizing previous results form Marché-Maurin, Corvaja-Demeio-Masser-Zannier and Ulmer-Urzúa. The result in the case of split semiabelian varieties has been obtained in a joint work with Ballini and Capuano.