The Selenium API doesn't provide a way to get a file downloaded on a remote machine.
But it's still possible with Selenium alone depending on the browser.
With Chrome the downloaded files can be listed by navigating chrome://downloads/ and retrieved with an injected <input type="file"> in the page :
from selenium import webdriver
from selenium.webdriver.support.ui import WebDriverWait
import os, time, base64
def get_downloaded_files(driver):
  if not driver.current_url.startswith("chrome://downloads"):
    driver.get("chrome://downloads/")
  return driver.execute_script( \
    "return downloads.Manager.get().items_   "
    "  .filter(e => e.state === 'COMPLETE')  "
    "  .map(e => e.filePath || e.file_path); " )
def get_file_content(driver, path):
  elem = driver.execute_script( \
    "var input = window.document.createElement('INPUT'); "
    "input.setAttribute('type', 'file'); "
    "input.hidden = true; "
    "input.onchange = function (e) { e.stopPropagation() }; "
    "return window.document.documentElement.appendChild(input); " )
  elem._execute('sendKeysToElement', {'value': [ path ], 'text': path})
  result = driver.execute_async_script( \
    "var input = arguments[0], callback = arguments[1]; "
    "var reader = new FileReader(); "
    "reader.onload = function (ev) { callback(reader.result) }; "
    "reader.onerror = function (ex) { callback(ex.message) }; "
    "reader.readAsDataURL(input.files[0]); "
    "input.remove(); "
    , elem)
  if not result.startswith('data:') :
    raise Exception("Failed to get file content: %s" % result)
  return base64.b64decode(result[result.find('base64,') + 7:])
capabilities_chrome = { \
    'browserName': 'chrome',
    # 'proxy': { \
     # 'proxyType': 'manual',
     # 'sslProxy': '50.59.162.78:8088',
     # 'httpProxy': '50.59.162.78:8088'
    # },
    'goog:chromeOptions': { \
      'args': [
      ],
      'prefs': { \
        # 'download.default_directory': "",
        # 'download.directory_upgrade': True,
        'download.prompt_for_download': False,
        'plugins.always_open_pdf_externally': True,
        'safebrowsing_for_trusted_sources_enabled': False
      }
    }
  }
driver = webdriver.Chrome(desired_capabilities=capabilities_chrome)
#driver = webdriver.Remote('http://127.0.0.1:5555/wd/hub', capabilities_chrome)
# download a pdf file
driver.get("https://www.mozilla.org/en-US/foundation/documents")
driver.find_element_by_css_selector("[href$='.pdf']").click()
# list all the completed remote files (waits for at least one)
files = WebDriverWait(driver, 20, 1).until(get_downloaded_files)
# get the content of the first file remotely
content = get_file_content(driver, files[0])
# save the content in a local file in the working directory
with open(os.path.basename(files[0]), 'wb') as f:
  f.write(content)
With Firefox, the files can be directly listed and retrieved by calling the browser API with a script by switching the context :
from selenium import webdriver
from selenium.webdriver.support.ui import WebDriverWait
import os, time, base64
def get_file_names_moz(driver):
  driver.command_executor._commands["SET_CONTEXT"] = ("POST", "/session/$sessionId/moz/context")
  driver.execute("SET_CONTEXT", {"context": "chrome"})
  return driver.execute_async_script("""
    var { Downloads } = Components.utils.import('resource://gre/modules/Downloads.jsm', {});
    Downloads.getList(Downloads.ALL)
      .then(list => list.getAll())
      .then(entries => entries.filter(e => e.succeeded).map(e => e.target.path))
      .then(arguments[0]);
    """)
  driver.execute("SET_CONTEXT", {"context": "content"})
def get_file_content_moz(driver, path):
  driver.execute("SET_CONTEXT", {"context": "chrome"})
  result = driver.execute_async_script("""
    var { OS } = Cu.import("resource://gre/modules/osfile.jsm", {});
    OS.File.read(arguments[0]).then(function(data) {
      var base64 = Cc["@mozilla.org/scriptablebase64encoder;1"].getService(Ci.nsIScriptableBase64Encoder);
      var stream = Cc['@mozilla.org/io/arraybuffer-input-stream;1'].createInstance(Ci.nsIArrayBufferInputStream);
      stream.setData(data.buffer, 0, data.length);
      return base64.encodeToString(stream, data.length);
    }).then(arguments[1]);
    """, path)
  driver.execute("SET_CONTEXT", {"context": "content"})
  return base64.b64decode(result)
capabilities_moz = { \
    'browserName': 'firefox',
    'marionette': True,
    'acceptInsecureCerts': True,
    'moz:firefoxOptions': { \
      'args': [],
      'prefs': {
        # 'network.proxy.type': 1,
        # 'network.proxy.http': '12.157.129.35', 'network.proxy.http_port': 8080,
        # 'network.proxy.ssl':  '12.157.129.35', 'network.proxy.ssl_port':  8080,      
        'browser.download.dir': '',
        'browser.helperApps.neverAsk.saveToDisk': 'application/octet-stream,application/pdf', 
        'browser.download.useDownloadDir': True, 
        'browser.download.manager.showWhenStarting': False, 
        'browser.download.animateNotifications': False, 
        'browser.safebrowsing.downloads.enabled': False, 
        'browser.download.folderList': 2,
        'pdfjs.disabled': True
      }
    }
  }
# launch Firefox
# driver = webdriver.Firefox(capabilities=capabilities_moz)
driver = webdriver.Remote('http://127.0.0.1:5555/wd/hub', capabilities_moz)
# download a pdf file
driver.get("https://www.mozilla.org/en-US/foundation/documents")
driver.find_element_by_css_selector("[href$='.pdf']").click()
# list all the downloaded files (waits for at least one)
files = WebDriverWait(driver, 20, 1).until(get_file_names_moz)
# get the content of the last downloaded file
content = get_file_content_moz(driver, files[0])
# save the content in a local file in the working directory
with open(os.path.basename(files[0]), 'wb') as f:
  f.write(content)