Prompt injection benchmarks assess whether large language models (LLMs) and agents resist malicious instructions embedded in external content. However, a system could perform well by rejecting attacks that obviously abandon the user's request, while still accepting changes that retain most of a legitimate answer but make it incorrect or harmful. Testing more instructions for unrelated outcomes would not necessarily reveal this weakness. We call attacks seeking responses designed to resemble legitimate answers while introducing incorrect or harmful changes near-target prompt injection. We introduce NTBench, the Near-Target Benchmark, which builds on legitimate tasks from existing datasets. For each task, a legitimate reference outcome guides the generation of target--instruction pairs, with separate tracks targeting incorrect and harmful outcomes in responses or agent tool invocations. Harmful targets can also accompany otherwise correct task completion. We combine LLM-based checks with human validation of the intended deviations, then assess whether injected instructions induce them using response judgments or tool-call checks, excluding deviations already observed without injection. We evaluate seven LLMs on ten datasets for language tasks and two agent benchmarks. Under a common budget of three attack executions per sample, both tracks achieve higher overall attack success rates than the fixed-target baseline for every evaluated model in each setting. On language tasks, the increases range from 9.3 to 35.8 percentage points for incorrect targets and 1.7 to 17.3 percentage points for harmful targets. These results show that resistance to the tested fixed-target attacks does not imply resistance to related incorrect or harmful outcomes, and that reference-guided targets broaden the failures revealed by robustness evaluation.

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