Large language models (LLMs) are capable of generating coherent summaries from very long contexts given a user query, and extracting and citing evidence spans helps improve the trustworthiness of these summaries. Whereas previous work has focused on evidence citation with fixed levels of granularity (e.g. sentence, paragraph, document, etc.), we propose to extract unstructured (i.e., spans of any length) evidence in order to acquire more relevant and consistent evidence than in the fixed granularity case. We show how existing systems struggle to copy and properly cite unstructured evidence, which also tends to be "lost-in-the-middle". To help models perform this task, we create the Summaries with Unstructured Evidence Text dataset (SUnsET), a synthetic dataset generated using a novel pipeline, which can be used as training supervision for unstructured evidence summarization. We demonstrate across 5 LLMs and 4 datasets spanning human written, synthetic, single, and multi-document settings that LLMs adapted with SUnsET generate more relevant and factually consistent evidence with their summaries, extract evidence from more diverse locations in their context, and can generate more relevant and consistent summaries than baselines with no fine-tuning and fixed granularity evidence. We release SUnsET and our generation code to the public.