An apparatus includes a housing, engagement slips, a tubular, a taper tap, a pin, and a slip activation member. The housing includes a profile that defines a path including a first end and a second end. The engagement slips are attached to the housing. The tubular passes through an opening of the housing. The taper tap is rotatable and connected to the housing. The pin is connected to the tubular and received by the profile of the housing. The tubular is translatable with respect to the housing based on the pin translating along the path defined by the profile. The slip activation member is connected to the tubular. The slip activation member is configured to move each of the engagement slips radially outward with respect to the housing when the pin translates to the second end of the path.