diff --git a/src/async.zsh b/src/async.zsh
index 814a185..f1877d3 100644
--- a/src/async.zsh
+++ b/src/async.zsh
@@ -10,8 +10,9 @@ _zsh_autosuggest_async_request() {
 
 	# If we've got a pending request, cancel it
 	if [[ -n "$_ZSH_AUTOSUGGEST_ASYNC_FD" ]] && { true <&$_ZSH_AUTOSUGGEST_ASYNC_FD } 2>/dev/null; then
-		# Close the file descriptor
+		# Close the file descriptor and remove the handler
 		exec {_ZSH_AUTOSUGGEST_ASYNC_FD}<&-
+		zle -F $_ZSH_AUTOSUGGEST_ASYNC_FD
 
 		# Zsh will make a new process group for the child process only if job
 		# control is enabled (MONITOR option)
@@ -49,10 +50,14 @@ _zsh_autosuggest_async_request() {
 # First arg will be fd ready for reading
 # Second arg will be passed in case of error
 _zsh_autosuggest_async_response() {
-	# Read everything from the fd and give it as a suggestion
-	zle autosuggest-suggest -- "$(cat <&$1)"
+	if [[ -z "$2" || "$2" == "hup" ]]; then
+		# Read everything from the fd and give it as a suggestion
+		zle autosuggest-suggest -- "$(cat <&$1)"
 
-	# Remove the handler and close the fd
+		# Close the fd
+		exec {1}<&-
+	fi
+
+	# Always remove the handler
 	zle -F "$1"
-	exec {1}<&-
 }
diff --git a/zsh-autosuggestions.zsh b/zsh-autosuggestions.zsh
index 191cda1..f94859e 100644
--- a/zsh-autosuggestions.zsh
+++ b/zsh-autosuggestions.zsh
@@ -689,8 +689,9 @@ _zsh_autosuggest_async_request() {
 
 	# If we've got a pending request, cancel it
 	if [[ -n "$_ZSH_AUTOSUGGEST_ASYNC_FD" ]] && { true <&$_ZSH_AUTOSUGGEST_ASYNC_FD } 2>/dev/null; then
-		# Close the file descriptor
+		# Close the file descriptor and remove the handler
 		exec {_ZSH_AUTOSUGGEST_ASYNC_FD}<&-
+		zle -F $_ZSH_AUTOSUGGEST_ASYNC_FD
 
 		# Zsh will make a new process group for the child process only if job
 		# control is enabled (MONITOR option)
@@ -728,12 +729,16 @@ _zsh_autosuggest_async_request() {
 # First arg will be fd ready for reading
 # Second arg will be passed in case of error
 _zsh_autosuggest_async_response() {
-	# Read everything from the fd and give it as a suggestion
-	zle autosuggest-suggest -- "$(cat <&$1)"
+	if [[ -z "$2" || "$2" == "hup" ]]; then
+		# Read everything from the fd and give it as a suggestion
+		zle autosuggest-suggest -- "$(cat <&$1)"
 
-	# Remove the handler and close the fd
+		# Close the fd
+		exec {1}<&-
+	fi
+
+	# Always remove the handler
 	zle -F "$1"
-	exec {1}<&-
 }
 
 #--------------------------------------------------------------------#