diff --git a/EasyJobsBase/src/jobs.jl b/EasyJobsBase/src/jobs.jl
index ac02ffb..90f315f 100644
--- a/EasyJobsBase/src/jobs.jl
+++ b/EasyJobsBase/src/jobs.jl
@@ -88,7 +88,10 @@ mutable struct ConditionalJob <: DependentJob
     parents::Set{AbstractJob}
     "These jobs runs after the current job."
     children::Set{AbstractJob}
-    function ConditionalJob(core::Think; name="", description="", username="")
+    skip_incomplete::Bool
+    function ConditionalJob(
+        core::Think, skip_incomplete=true; name="", description="", username=""
+    )
         return new(
             uuid1(),
             core,
@@ -102,6 +105,7 @@ mutable struct ConditionalJob <: DependentJob
             0,
             Set(),
             Set(),
+            skip_incomplete,
         )
     end
 end
@@ -122,9 +126,9 @@ mutable struct ArgDependentJob <: DependentJob
     parents::Set{AbstractJob}
     "These jobs runs after the current job."
     children::Set{AbstractJob}
-    succeededonly::Bool
+    skip_incomplete::Bool
     function ArgDependentJob(
-        core::Think, succeededonly=true; name="", description="", username=""
+        core::Think, skip_incomplete=true; name="", description="", username=""
     )
         return new(
             uuid1(),
@@ -139,7 +143,7 @@ mutable struct ArgDependentJob <: DependentJob
             0,
             Set(),
             Set(),
-            succeededonly,
+            skip_incomplete,
         )
     end
 end
diff --git a/EasyJobsBase/src/run.jl b/EasyJobsBase/src/run.jl
index 4eae2cd..d83e454 100644
--- a/EasyJobsBase/src/run.jl
+++ b/EasyJobsBase/src/run.jl
@@ -1,6 +1,6 @@
 using Thinkers: TimeoutException, ErrorInfo, reify!, setargs!, haserred, _kill
 
-export run!, execute!, kill!
+export shouldrun, run!, execute!, kill!
 
 # See https://github.com/MineralsCloud/SimpleWorkflows.jl/issues/137
 """
@@ -123,16 +123,14 @@ prepare!(::AbstractJob) = nothing  # No op
 function prepare!(job::ArgDependentJob)
     # Use previous results as arguments
     args = if countparents(job) == 1
-        result = getresult(only(eachparent(job)))
-        if isnothing(result)  # Parent job is pending or still running
-            # This means `job.succeededonly` must be `true` based on the logic
-            # Keep the arguments unchanged
-            @warn "the parent job is pending or still running! No arguments will be set!"
-        else  # Parent job has succeeded or failed
-            something(result)
+        parent = only(eachparent(job))
+        if issucceeded(parent)
+            something(getresult(parent))
+        else
+            error("the parent job has failed!")
         end
     else  # > 1
-        parents = if job.succeededonly
+        parents = if job.skip_incomplete
             Iterators.filter(issucceeded, eachparent(job))
         else
             eachparent(job)
@@ -143,15 +141,15 @@ function prepare!(job::ArgDependentJob)
     return nothing
 end
 
-shouldrun(::AbstractJob) = true
-shouldrun(job::ConditionalJob) =
-    countparents(job) >= 1 && all(issucceeded(parent) for parent in eachparent(job))
-function shouldrun(job::ArgDependentJob)
-    if job.succeededonly
-        return countparents(job) >= 1
+shouldrun(::IndependentJob) = true
+function shouldrun(job::Union{ConditionalJob,ArgDependentJob})
+    if countparents(job) < 1
+        return false
+    end
+    if job.skip_incomplete
+        return all(issucceeded(parent) for parent in eachparent(job))
     else
-        return countparents(job) >= 1 &&
-               all(issucceeded(parent) for parent in eachparent(job))
+        return all(isexited(parent) for parent in eachparent(job))
     end
 end
 
diff --git a/EasyJobsBase/test/run.jl b/EasyJobsBase/test/run.jl
index 2d9f6d4..3438206 100644
--- a/EasyJobsBase/test/run.jl
+++ b/EasyJobsBase/test/run.jl
@@ -111,14 +111,17 @@ end
     j = ArgDependentJob(Thunk(f₂, 3), false; username="he", name="j")
     k = ArgDependentJob(Thunk(f₃, 6), false; username="she", name="k")
     i → j → k
-    @test_throws AssertionError run!(j)
+    @test !shouldrun(j)
+    @test !shouldrun(k)
     exec = run!(i)
     wait(exec)
     @test getresult(i) == Some(25)
-    @test_throws AssertionError run!(k)
+    @test shouldrun(j)
+    @test !shouldrun(k)
     exec = run!(j)
     wait(exec)
     @test getresult(j) == Some(26)
+    @test shouldrun(k)
     exec = run!(k)
     wait(exec)
     @test getresult(k) == Some(13.0)
@@ -134,15 +137,14 @@ end
     k = Job(Thunk(f₃, 6); username="she", name="k")
     l = ArgDependentJob(Thunk(f₄, ()); username="she", name="me")
     (i, j, k) .→ l
-    exec = run!(l)
-    wait(exec)
-    @test isfailed(l)
+    @test !shouldrun(l)
     execs = map((i, j, k)) do job
         run!(job)
     end
     for exec in execs
         wait(exec)
     end
+    @test shouldrun(l)
     l.core = Thunk(l.core)
     exec = run!(l)
     wait(exec)
@@ -150,12 +152,13 @@ end
     @test getresult(j) == Some(4)
     @test getresult(k) == Some(3.0)
     @test getresult(l) == Some(32.0)
-    @testset "Change `succeededonly` to `false`" begin
+    @testset "Change `skip_incomplete` to `false`" begin
         i = Job(Thunk(f₁, 5); username="me", name="i")
         j = Job(Thunk(f₂, 3); username="he", name="j")
         k = Job(Thunk(f₃, 6); username="she", name="k")
         l = ArgDependentJob(Thunk(f₄, ()), false; username="she", name="me")
         (i, j, k) .→ l
+        @test !shouldrun(l)
+        @test_throws AssertionError run!(l)
     end
-    @test_throws AssertionError run!(l)
 end