Previous studies have surveyed the potential impact of loss-of-function (LoF) variants and identified LoF-tolerant protein-coding genes. However, the tolerance of human genomes to losing enhancers has not yet been evaluated. Here we present the catalog of LoF-tolerant enhancers using structural variants from whole-genome sequences. Using a conservative approach, we estimate that individual human genomes possess at least 28 LoF-tolerant enhancers on average. We assessed the properties of LoF-tolerant enhancers in a unified regulatory network constructed by integrating tissue-specific enhancers and gene-gene interactions. We find that LoF-tolerant enhancers tend to be more tissue-specific and regulate fewer and more dispensable genes relative to other enhancers. They are enriched in immune-related cells while enhancers with low LoF-tolerance are enriched in kidney and brain/neuronal stem cells. We developed a supervised learning approach to predict the LoF-tolerance of all enhancers, which achieved an area under the receiver operating characteristics curve (AUROC) of 98%. We predict 3,519 more enhancers would be likely tolerant to LoF and 129 enhancers that would have low LoF-tolerance. Our predictions are supported by a known set of disease enhancers and novel deletions from PacBio sequencing. The LoF-tolerance scores provided here will serve as an important reference for disease studies.