While tensor-based methods excel at Direction-of-Arrival (DOA) estimation, their performance degrades severely with faulty or sparse arrays that violate the required manifold structure. To address this challenge, we propose Tensor Completion for Defective Arrays (TCDA), a robust algorithm that reformulates the physical imperfection problem as a data recovery task within a virtual tensor space. We present a detailed derivation for constructing an incomplete third-order Parallel Factor Analysis (PARAFAC) tensor from the faulty array signals via subarray partitioning, cross-correlation, and dimensional reshaping. Leveraging the tensor's inherent low-rank structure, an Alternating Least Squares (ALS)-based algorithm directly recovers the factor matrices embedding the DOA parameters from the incomplete observations. This approach provides a software-defined 'self-healing' capability, demonstrating exceptional robustness against random element failures without requiring additional processing steps for DOA estimation.