diff --git a/llvm/include/llvm/IR/InstrTypes.h b/llvm/include/llvm/IR/InstrTypes.h
--- a/llvm/include/llvm/IR/InstrTypes.h
+++ b/llvm/include/llvm/IR/InstrTypes.h
@@ -1756,6 +1756,13 @@
   bool onlyReadsMemory() const {
     return doesNotAccessMemory() || hasFnAttr(Attribute::ReadOnly);
   }
+
+  /// Returns true if this function is guaranteed to return.
+  bool willReturn() const {
+    return hasFnAttr(Attribute::WillReturn) ||
+           hasFnAttr(Attribute::MustProgress);
+  }
+
   void setOnlyReadsMemory() {
     addAttribute(AttributeList::FunctionIndex, Attribute::ReadOnly);
   }
diff --git a/llvm/lib/Transforms/Utils/Local.cpp b/llvm/lib/Transforms/Utils/Local.cpp
--- a/llvm/lib/Transforms/Utils/Local.cpp
+++ b/llvm/lib/Transforms/Utils/Local.cpp
@@ -413,6 +413,12 @@
     return true;
   }
 
+  if (auto *CB = dyn_cast<CallBase>(I))
+    // Treat calls that may not return as alive (they could loop infinitely),
+    // unless the containing function must make progress.
+    if (!I->getParent()->getParent()->mustProgress() && !CB->willReturn())
+      return false;
+
   if (!I->mayHaveSideEffects())
     return true;
 
diff --git a/llvm/test/Transforms/Inline/dead-calls-mustprogress.ll b/llvm/test/Transforms/Inline/dead-calls-mustprogress.ll
--- a/llvm/test/Transforms/Inline/dead-calls-mustprogress.ll
+++ b/llvm/test/Transforms/Inline/dead-calls-mustprogress.ll
@@ -46,6 +46,10 @@
 define void @caller_no_mustprogress() ssp {
 ; CHECK-LABEL: @caller_no_mustprogress(
 ; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br label [[WHILE_BODY_I:%.*]]
+; CHECK:       while.body.i:
+; CHECK-NEXT:    br label [[WHILE_BODY_I]]
+; CHECK:       readnone.exit:
 ; CHECK-NEXT:    ret void
 ;
 entry: