The insertion or deletion (indel) of amino acids has a variety of effects on protein function, ranging from disease-forming changes to gaining new functions. Despite their importance, indels have not been systematically characterized towards protein engineering or modification goals. In the present work, we focus on deletions composed of multiple contiguous amino acids (mAA-dels) and their effects on the protein (mutant) folding ability. Our analysis reveals that the mutant retains the native fold when the mAA-del obeys well-defined structural dynamics properties: localization in intrinsically flexible regions, showing low resistance to mechanical stress, and separation from allosteric signaling paths. Motivated by the possibility of distinguishing the features that underlie the adaptability of proteins to mAA-dels, and by the rapid evaluation of these features using elastic network models, we developed a positive-unlabeled learning-based classifier that can be adopted for protein design purposes. Trained on a consolidated set of features, including those reflecting the intrinsic dynamics of the regions where the mAA-dels occur, the new classifier yields a high recall of 84.3% for identifying mAA-dels that are stably tolerated by the protein. The comparative examination of the relative contribution of different features to the prediction reveals the dominant role of structural dynamics in enabling the adaptation of the mutant to mAA-del without disrupting the native fold.