It is shown that two fundamentally different phenomena, the bound states in continuum and the spectral singularity (or time-reversed spectral singularity), can occur simultaneously. This can be achieved, in particular, in a rectangular core dielectric waveguide with embedded active (or absorbing) layer. In such a system a two-dimensional bound state in a continuum is created in the plane of a waveguide cross section and it is emitted or absorbed along the waveguide core. The idea can be used for experimental implementation of a laser or a coherent-perfect-absorber for photonic bound state that resides in a continuous spectrum.Unusual points in spectra of optical systems, i.e. isolated points, which do not exist in a generic situation and may require special engineering of the system, attract increasing attention during the last years. For either Hermitian or non-Hermitian systems these are, in particular, the bound states in continuum (BIC), which were predicted almost a century ago [1] and acquired great experimental and practical importance [2][3][4][5][6] in recent years (see also [7] and reference therein). In the case of non-Hermitian optical systems, the continuum spectrum can also host either spectral singularities [8,9], at which the system behaves like a laser, and time-reversed spectral singularities at which the system becomes a coherent-perfect-absorber (CPA) for light at a given wavelength [10][11][12].From the mathematical point of view, either BIC or spectral singularities (for the sake of brevity under spectral singularities here we also understand time-reversed spectral singularities) represent isolated points inside the continuous spectrum, requiring fine tuning of the parameters to be achievable in principle. From the physical point of view in the case of CPA and BIC the parameters of the scattering potential must be chosen to ensure a delicate condition of destructive interference of outgoing radiation completely canceling it at the infinities. Thus, it looks very unlikely to satisfy the conditions for a BIC and either laser or CPA at the same wavelength (just because this would require too many free system parameters). The aim of this Letter is to show that in practice this is not necessarily so, and the conditions for a BIC and for a spectral singularity can be met simultaneously. In other words one can create a laser or a CPA for a BIC. We explore the waveguide geometry where a two-dimensional (2D) BIC is created in the plane orthogonal to the waveguide axis; and a spectral singularity is found in the spectrum of the longitudinal waves. Thus although both phenomena occur simultaneously, they remain conceptually different. Nevertheless, as shown below, the phenomena of BIC and spectral singularity are correlated for a guided wave due to the energy exchange between the transverse and longitudinal directions in a waveguide.Of late, a BIC laser was demonstrated experimentally [13], although using a mechanism which differs from the one presented in this Letter. A two-dimensional lattice was ill...